Difference between revisions of "Velocity-Time Graph"
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: On a '''velocity-time graph''' the [[velocity]] is plotted on the [[y-axis]] and the [[time]] is plotted on the [[x-axis]]. | : On a '''velocity-time graph''' the [[velocity]] is plotted on the [[y-axis]] and the [[time]] is plotted on the [[x-axis]]. | ||
: A '''velocity-time graph''' can be used to calculate the [[acceleration]] of an [[object]] or the [[distance]] travelled by the [[object]]. | : A '''velocity-time graph''' can be used to calculate the [[acceleration]] of an [[object]] or the [[distance]] travelled by the [[object]]. | ||
− | + | : The [[gradient]] of a '''velocity-time graph''' is the same as the [[acceleration]]. | |
+ | : The [[area]] under the curve on a '''velocity-time graph''' is the [[distance]] travelled by an [[object]]. | ||
{| class="wikitable" | {| class="wikitable" | ||
Line 22: | Line 23: | ||
| style="height:20px; width:200px; text-align:center;" |[[Deceleration]] is shown by a negative [[gradient]]. | | style="height:20px; width:200px; text-align:center;" |[[Deceleration]] is shown by a negative [[gradient]]. | ||
|} | |} | ||
− | |||
===Example Calculations=== | ===Example Calculations=== | ||
====Calculating Acceleration==== | ====Calculating Acceleration==== | ||
− | : The | + | : The [[acceleration]] can be calculated from a '''velocity-time graph''' by reading the [[graph]] and using the equation <math>a=\frac{v-u}{t}</math>. |
+ | {| class="wikitable" | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''Calculate the [[acceleration]] of the object in this journey.''' | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''Calculate the [[acceleration]] of the object in this journey.''' | ||
+ | |- | ||
+ | |[[File:vtGraphCalculateAcceleration1.png|center|300px]] | ||
+ | |[[File:vtGraphCalculateAcceleration2.png|center|300px]] | ||
+ | |- | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''State the known [[variable]]s.''' | ||
+ | v = 40m/s | ||
+ | |||
+ | u = 20m/s | ||
+ | |||
+ | t = 8s | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''State the known [[variable]]s.''' | ||
+ | v = 10m/s | ||
+ | |||
+ | u = 40m/s | ||
+ | |||
+ | t = 8s | ||
+ | |- | ||
+ | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].''' | ||
+ | |||
+ | <math>a = \frac{v-u}{t}</math> | ||
+ | |||
+ | <math>a = \frac{40-20}{8}</math> | ||
+ | |||
+ | <math>a = \frac{20}{8}</math> | ||
+ | |||
+ | <math>a = 2.5m/s/s</math> | ||
+ | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].''' | ||
+ | |||
+ | <math>a = \frac{v-u}{t}</math> | ||
+ | |||
+ | <math>a = \frac{10-40}{8}</math> | ||
+ | |||
+ | <math>a = \frac{-30}{8}</math> | ||
+ | |||
+ | <math>a = -3.75m/s/s</math> | ||
+ | |} | ||
+ | |||
+ | {| class="wikitable" | ||
+ | | style="height:20px; width:500px; text-align:left;" colspan = "3"|'''Calculate the [[acceleration]] of the [[object]] at each stage in this journey.''' | ||
+ | |- | ||
+ | | style="height:20px; width:500px; text-align:left;" colspan = "3"|[[File:vtGraph1.png|centre|500px]] | ||
+ | |- | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''A''' | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''B''' | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''C''' | ||
+ | |- | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''State the known [[variable]]s.''' | ||
+ | [[File:vtGraphCalculateAcceleration3.png|centre|150px]] | ||
+ | v = 30m/s | ||
+ | |||
+ | u = 0m/s | ||
+ | |||
+ | t = 2s | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''State the known [[variable]]s.''' | ||
+ | [[File:vtGraphCalculateAcceleration3.png|centre|150px]] | ||
+ | v = 30m/s | ||
+ | |||
+ | u = 30m/s | ||
+ | |||
+ | t = 3s | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''State the known [[variable]]s.''' | ||
+ | [[File:vtGraphCalculateAcceleration3.png|centre|150px]] | ||
+ | v = 50m/s | ||
+ | |||
+ | u = 30m/s | ||
+ | |||
+ | t = 3s | ||
+ | |- | ||
+ | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].''' | ||
+ | |||
+ | <math>a = \frac{v-u}{t}</math> | ||
+ | |||
+ | <math>a = \frac{30-0}{2}</math> | ||
+ | |||
+ | <math>a = \frac{30}{2}</math> | ||
+ | |||
+ | <math>a = 15m/s/s</math> | ||
+ | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].''' | ||
+ | |||
+ | <math>a = \frac{v-u}{t}</math> | ||
+ | |||
+ | <math>a = \frac{30-30}{3}</math> | ||
+ | |||
+ | <math>a = \frac{0}{3}</math> | ||
+ | |||
+ | <math>a = 0m/s/s</math> | ||
+ | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].''' | ||
+ | |||
+ | <math>a = \frac{v-u}{t}</math> | ||
+ | |||
+ | <math>a = \frac{50-30}{3}</math> | ||
+ | |||
+ | <math>a = \frac{20}{3}</math> | ||
+ | |||
+ | <math>a = 6.7m/s/s</math> | ||
+ | |} | ||
+ | |||
+ | ====Calculating Distance Travelled==== | ||
+ | : The [[distance]] travelled can be calculated from a '''velocity-time graph''' by breaking the [[graph]] into simple shapes and finding the [[area]] of those shapes. This may use the equations <math>area = base \times height</math> for rectangular shapes and <math>area = \frac{base \times height}{2}</math> for triangular shapes. | ||
+ | |||
{| class="wikitable" | {| class="wikitable" | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''Calculate the [[distance]] travelled by the [[object]] in this journey.''' | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''Calculate the [[distance]] travelled by the [[object]] in this journey.''' | ||
|- | |- | ||
− | |[[File: | + | |[[File:vtGraphCalculateArea1.png|center|300px]] |
− | |[[File: | + | |[[File:vtGraphCalculateArea2.png|center|300px]] |
|- | |- | ||
− | | style="height:20px; width: | + | | style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities''' |
+ | base = 8s | ||
− | | style="height:20px; width: | + | height = 30m/s |
+ | | style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities''' | ||
+ | base = 8s | ||
+ | height = 40m/s | ||
+ | |- | ||
+ | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].''' | ||
+ | |||
+ | <math>area = b \times h</math> | ||
+ | |||
+ | <math>area = 8 \times 30</math> | ||
+ | |||
+ | <math>area = distance = 250m</math> | ||
+ | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].''' | ||
+ | |||
+ | <math>area = \frac{b \times h}{2}</math> | ||
+ | |||
+ | <math>area = \frac{8 \times 40}{2}</math> | ||
+ | |||
+ | <math>area = \frac{320}{2}</math> | ||
+ | |||
+ | <math>area = distance = 160m</math> | ||
|} | |} | ||
{| class="wikitable" | {| class="wikitable" | ||
+ | | style="height:20px; width:500px; text-align:left;" colspan = "3"|'''Calculate the distance travelled by the [[object]] at each stage in this journey.''' | ||
+ | |- | ||
+ | | style="height:20px; width:500px; text-align:left;" colspan = "3"|[[File:vtGraph1.png|centre|500px]] | ||
+ | |- | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''A''' | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''B''' | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''C''' | ||
|- | |- | ||
− | |[[File: | + | | style="height:20px; width:300px; text-align:left;" |'''State the known [[variable]]s.''' |
− | |[[File: | + | [[File:vtGraphCalculateArea3.png|centre|150px]] |
+ | b = 2s | ||
+ | |||
+ | h = 30m/s | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''State the known [[variable]]s.''' | ||
+ | [[File:vtGraphCalculateArea3.png|centre|150px]] | ||
+ | b = 3s | ||
+ | |||
+ | h = 30m/s | ||
+ | | style="height:20px; width:300px; text-align:left;" |'''State the known [[variable]]s.''' | ||
+ | [[File:vtGraphCalculateArea3.png|centre|150px]] | ||
+ | b = 3s | ||
+ | |||
+ | h<sub>1</sub> = 30m/s | ||
+ | |||
+ | h<sub>2</sub> = 50m/s | ||
|- | |- | ||
− | | style="height:20px; width: | + | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].''' |
+ | |||
+ | <math>area = \frac{b \times h}{2}</math> | ||
+ | |||
+ | <math>area = \frac{2 \times 30}{2}</math> | ||
+ | |||
+ | <math>area = \frac{60}{2}</math> | ||
− | | style="height:20px; width: | + | <math>area = distance = 30m</math> |
+ | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].''' | ||
+ | <math>area = b \times h</math> | ||
+ | |||
+ | <math>area = 3 \times 30</math> | ||
+ | |||
+ | <math>area = distance = 90m</math> | ||
+ | | style="height:20px; width:200px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].''' | ||
+ | |||
+ | <math>area = b \times h</math> | ||
+ | |||
+ | <math>area = 3 \times 30</math> | ||
+ | |||
+ | <math>area = distance = 90m</math> for yellow shaded area. | ||
+ | |||
+ | <math>area = \frac{b \times h}{2}</math> | ||
+ | |||
+ | <math>area = \frac{3 \times (50-30)}{2}</math> | ||
+ | |||
+ | <math>area = \frac{60}{2}</math> | ||
+ | |||
+ | <math>area = distance = 30m</math> for red area. | ||
+ | |||
+ | ''Total distance = 120m'' | ||
|} | |} | ||
+ | |||
+ | ===References=== | ||
+ | ====AQA==== | ||
+ | |||
+ | :[https://www.amazon.co.uk/gp/product/0008158770/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=0008158770&linkCode=as2&tag=nrjc-21&linkId=ec31595e720e1529e49876c3866fff6e ''Velocity-time graph, pages 148-9, GCSE Physics; Student Book, Collins, AQA ''] | ||
+ | :[https://www.amazon.co.uk/gp/product/1782945598/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945598&linkCode=as2&tag=nrjc-21&linkId=ad276ad49df77ab4b40ab4fd0fe10400 ''Velocity-time graphs, page 211, GCSE Combined Science; The Revision Guide, CGP, AQA ''] | ||
+ | :[https://www.amazon.co.uk/gp/product/019835939X/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=019835939X&linkCode=as2&tag=nrjc-21&linkId=57e96876985fc39b1a3d8a3e3dc238b6 ''Velocity-time graphs, pages 136, 138-141, GCSE Physics; Third Edition, Oxford University Press, AQA ''] | ||
+ | :[https://www.amazon.co.uk/gp/product/1471851370/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1471851370&linkCode=as2&tag=nrjc-21&linkId=01c69b0ae058f809cf636033e6ba793e ''Velocity-time graphs, pages 152-3, GCSE Physics, Hodder, AQA ''] | ||
+ | :[https://www.amazon.co.uk/gp/product/1782946403/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782946403&linkCode=as2&tag=nrjc-21&linkId=32a0abb60dff015b15b50e9b1d7b4644 ''Velocity-time graphs, pages 155-157, GCSE Combined Science Trilogy; Physics, CGP, AQA ''] | ||
+ | :[https://www.amazon.co.uk/gp/product/1782945970/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945970&linkCode=as2&tag=nrjc-21&linkId=a120d24dcc7cc7a58192069a3aafc1d2 ''Velocity-time graphs, pages 186-188, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA ''] | ||
+ | :[https://www.amazon.co.uk/gp/product/1471851362/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1471851362&linkCode=as2&tag=nrjc-21&linkId=7d78d70a2044ee9982dae010c94af92a ''Velocity-time graphs, pages 230-1, 234, GCSE Combined Science Trilogy 2, Hodder, AQA ''] | ||
+ | :[https://www.amazon.co.uk/gp/product/178294558X/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=178294558X&linkCode=as2&tag=nrjc-21&linkId=f0dfb66dafcb0c6e9449e7b1a4ae1ac484 ''Velocity-time graphs, pages 62, 63, GCSE Physics; The Revision Guide, CGP, AQA ''] | ||
+ | :[https://www.amazon.co.uk/gp/product/1782946403/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782946403&linkCode=as2&tag=nrjc-21&linkId=32a0abb60dff015b15b50e9b1d7b4644 ''Velocity-time graphs; area under, pages 156, 157, GCSE Combined Science Trilogy; Physics, CGP, AQA ''] | ||
+ | :[https://www.amazon.co.uk/gp/product/1782945970/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945970&linkCode=as2&tag=nrjc-21&linkId=a120d24dcc7cc7a58192069a3aafc1d2 ''Velocity-time graphs; area under, pages 187, 188, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA ''] | ||
+ | :[https://www.amazon.co.uk/gp/product/1782945970/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945970&linkCode=as2&tag=nrjc-21&linkId=a120d24dcc7cc7a58192069a3aafc1d2 ''Velocity-time graphs; for falling objects, page 192, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA ''] | ||
+ | |||
+ | ====OCR==== | ||
+ | :[https://www.amazon.co.uk/gp/product/1782945695/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945695&linkCode=as2&tag=nrjc-21&linkId=ceafcc80bcad6b6754ee97a0c7ceea53 ''Velocity-time graphs, page 162, Gateway GCSE Combined Science; The Revision Guide, CGP, OCR ''] | ||
+ | :[https://www.amazon.co.uk/gp/product/1782945687/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945687&linkCode=as2&tag=nrjc-21&linkId=9a598e52189317a20311d7a632747bc9 ''Velocity-time graphs, page 25, Gateway GCSE Physics; The Revision Guide, CGP, OCR ''] |
Latest revision as of 10:59, 25 December 2019
Contents
Key Stage 4
Meaning
A velocity-time graph is a graph that shows how the velocity of an object changes with time.
About Velocity Time Graphs
- Velocity-time graphs give information about the journey taken by an object.
- On a velocity-time graph the velocity is plotted on the y-axis and the time is plotted on the x-axis.
- A velocity-time graph can be used to calculate the acceleration of an object or the distance travelled by the object.
- The gradient of a velocity-time graph is the same as the acceleration.
- The area under the curve on a velocity-time graph is the distance travelled by an object.
Constant Velocity | Accelerating | Decelerating |
A gradient of zero shows the object is travelling at a constant velocity. | Acceleration is shown by a positive gradient. | Deceleration is shown by a negative gradient. |
Example Calculations
Calculating Acceleration
- The acceleration can be calculated from a velocity-time graph by reading the graph and using the equation \(a=\frac{v-u}{t}\).
Calculate the acceleration of the object in this journey. | Calculate the acceleration of the object in this journey. |
State the known variables.
v = 40m/s u = 20m/s t = 8s |
State the known variables.
v = 10m/s u = 40m/s t = 8s |
2. Substitute the numbers into the equation and solve.
\(a = \frac{v-u}{t}\) \(a = \frac{40-20}{8}\) \(a = \frac{20}{8}\) \(a = 2.5m/s/s\) |
2. Substitute the numbers into the equation and solve.
\(a = \frac{v-u}{t}\) \(a = \frac{10-40}{8}\) \(a = \frac{-30}{8}\) \(a = -3.75m/s/s\) |
Calculate the acceleration of the object at each stage in this journey. | ||
A | B | C |
State the known variables.
v = 30m/s u = 0m/s t = 2s |
State the known variables.
v = 30m/s u = 30m/s t = 3s |
State the known variables.
v = 50m/s u = 30m/s t = 3s |
2. Substitute the numbers into the equation and solve.
\(a = \frac{v-u}{t}\) \(a = \frac{30-0}{2}\) \(a = \frac{30}{2}\) \(a = 15m/s/s\) |
2. Substitute the numbers into the equation and solve.
\(a = \frac{v-u}{t}\) \(a = \frac{30-30}{3}\) \(a = \frac{0}{3}\) \(a = 0m/s/s\) |
2. Substitute the numbers into the equation and solve.
\(a = \frac{v-u}{t}\) \(a = \frac{50-30}{3}\) \(a = \frac{20}{3}\) \(a = 6.7m/s/s\) |
Calculating Distance Travelled
- The distance travelled can be calculated from a velocity-time graph by breaking the graph into simple shapes and finding the area of those shapes. This may use the equations \(area = base \times height\) for rectangular shapes and \(area = \frac{base \times height}{2}\) for triangular shapes.
Calculate the distance travelled by the object in this journey. | Calculate the distance travelled by the object in this journey. |
1. State the known quantities
base = 8s height = 30m/s |
1. State the known quantities
base = 8s height = 40m/s |
2. Substitute the numbers into the equation and solve.
\(area = b \times h\) \(area = 8 \times 30\) \(area = distance = 250m\) |
2. Substitute the numbers into the equation and solve.
\(area = \frac{b \times h}{2}\) \(area = \frac{8 \times 40}{2}\) \(area = \frac{320}{2}\) \(area = distance = 160m\) |
Calculate the distance travelled by the object at each stage in this journey. | ||
A | B | C |
State the known variables.
b = 2s h = 30m/s |
State the known variables.
b = 3s h = 30m/s |
State the known variables.
b = 3s h1 = 30m/s h2 = 50m/s |
2. Substitute the numbers into the equation and solve.
\(area = \frac{b \times h}{2}\) \(area = \frac{2 \times 30}{2}\) \(area = \frac{60}{2}\) \(area = distance = 30m\) |
2. Substitute the numbers into the equation and solve.
\(area = b \times h\) \(area = 3 \times 30\) \(area = distance = 90m\) |
2. Substitute the numbers into the equation and solve.
\(area = b \times h\) \(area = 3 \times 30\) \(area = distance = 90m\) for yellow shaded area. \(area = \frac{b \times h}{2}\) \(area = \frac{3 \times (50-30)}{2}\) \(area = \frac{60}{2}\) \(area = distance = 30m\) for red area. Total distance = 120m |
References
AQA
- Velocity-time graph, pages 148-9, GCSE Physics; Student Book, Collins, AQA
- Velocity-time graphs, page 211, GCSE Combined Science; The Revision Guide, CGP, AQA
- Velocity-time graphs, pages 136, 138-141, GCSE Physics; Third Edition, Oxford University Press, AQA
- Velocity-time graphs, pages 152-3, GCSE Physics, Hodder, AQA
- Velocity-time graphs, pages 155-157, GCSE Combined Science Trilogy; Physics, CGP, AQA
- Velocity-time graphs, pages 186-188, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA
- Velocity-time graphs, pages 230-1, 234, GCSE Combined Science Trilogy 2, Hodder, AQA
- Velocity-time graphs, pages 62, 63, GCSE Physics; The Revision Guide, CGP, AQA
- Velocity-time graphs; area under, pages 156, 157, GCSE Combined Science Trilogy; Physics, CGP, AQA
- Velocity-time graphs; area under, pages 187, 188, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA
- Velocity-time graphs; for falling objects, page 192, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA