Velocity-Time Graph
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 |
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| 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. | ||
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| 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.
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| Calculate the distance travelled by the object in this journey. | Calculate the distance travelled by the object in this journey. |