Difference between revisions of "Velocity-Time Graph"

Revision as of 12:46, 14 February 2019

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. \(a = \frac{v-u}{t}\) \(a = \frac{10-40}{8}\) \(a = \frac{-30}{8}\) \(a = -3.75m/s/s\)

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 \(a = b \times h\) for rectangular shapes and \(a = \frac{b \times h}{2}\) for triangular shapes.


Calculate the distance travelled by the object in this journey.	Calculate the distance travelled by the object in this journey.

@@ Line 28: / Line 28: @@
 : 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;" |'''Calculate the [[acceleration]] of the object in this journey.'''
+| 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>
-| style="height:20px; width:300px; text-align:left;" |'''Calculate the [[acceleration]] of the object in this journey.'''
+<math>a = \frac{-30}{8}</math>
+<math>a = -3.75m/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>a = b \times h</math> for rectangular shapes and <math>a = \frac{b \times h}{2}</math> for triangular shapes.