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===Example Calculations===
====Calculating Acceleration====
: 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:vtGraphCalculation1vtGraphCalculateAcceleration1.png|center|300px]]|[[File:vtGraphCalculation2vtGraphCalculateAcceleration2.png|center|300px]]
|-
| style="height:20px; width:300px; text-align:left;" |'''Calculate State the known [[accelerationvariable]] of the object in the first 10 seconds of the journeys.'''v = 40m/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"
| 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:vtGraphCalculateArea1.png|center|300px]]
|[[File:vtGraphCalculateArea2.png|center|300px]]
|-
| style="height:20px; width:200px; text-align:left;" |'''1. State the known quantities'''
base = 8s
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"
| style="height:20px; width:500px; text-align:left;" colspan = "3"|'''Calculate the distance travelled by the [[object]] at each stage in this journey.'''
|-
|[[Filestyle="height:20px; width:500px; text-align:vtGraphCalculation1.png|center|300px]]left;" colspan = "3"|[[File:vtGraphCalculation2vtGraph1.png|centercentre|300px500px]]
|-
| style="height:20px; width:300px; text-align:left;" |'''Calculate 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.'''[[distanceFile:vtGraphCalculateArea3.png|centre|150px]] travelled by b = 2s h = 30m/s| style="height:20px; width:300px; text-align:left;" |'''State the known [[objectvariable]]s.'''[[File:vtGraphCalculateArea3.png|centre|150px]] in b = 3s h = 30m/s| style="height:20px; width:300px; text-align:left;" |'''State the first 20 seconds the entire journeyknown [[variable]]s.'''[[File:vtGraphCalculateArea3.png|centre|150px]]b = 3s
h<sub>2</sub> = 50m/s
|-
| 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>
<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 '']