P5 O) Velocity Time Graphs – Part 2
Sometimes in the exam you will be given a question that asks you to draw a velocity time graph. The best way to explain how to draw a velocity time graph is through an example.
Example 1
Draw a velocity time graph for the information that is given below:
- A car is initially stationary.
- The car then accelerates at a constant rate until it reaches a velocity of 14 m/s at 11 seconds.
- The car continues at a velocity of 14 m/s for 8 seconds.
- The car then accelerates again at a constant rate until it reaches a velocity of 20 m/s at 28 seconds.
- The car then decelerates at a constant rate until it is stationary. The car takes 16 seconds to decelerate.
An empty velocity time graph is shown below (click here for a printable version of this velocity time graph).
The second point tells us that the car accelerates at a constant rate until it reaches a velocity of 14 m/s at 11 seconds. Therefore, we mark the point with a velocity of 14 m/s and 11 seconds on the velocity time graph. The car is accelerating at a constant rate, which means that we have a straight line connecting the origin and the point that we have just marked.
We are able to work out acceleration from a velocity time graph. Acceleration is the rate of change in an objects velocity. A positive value for acceleration means that the velocity of an object is increasing. A negative value for acceleration means that the velocity of an object is decreasing; the object is decelerating.
The gradient of the line on a velocity time graph tells us the acceleration of the object. We work out the gradient of the line in the normal way.
The change in velocity of an object is measured in “metre per second” and time is measured in “seconds”. This means that the acceleration of an object is measured in metres per second per second, which can be written as m/s2.
Let’s have a look at finding the acceleration from a velocity time graph.
Work out the acceleration for the first 4 seconds and the final 3 seconds for the velocity time graph below.
In order to work out the acceleration, we need to work out the gradient of the line. We work out the gradient of a line by choosing two points on the line and then we sub these points into the gradient equation. I am going to choose the start and the end of the line; my two points are (0,0) and (4, 6).
The gradient is 1.5, which tells us that the rate of acceleration is 1.5 m/s2. This means that the velocity of the object will increase by 1.5 m/s every second.
We work out the acceleration for the final 3 seconds by finding the gradient of the line. The two points on the line that I am going to choose are the start of the final 3 seconds and the end of the final 3 seconds; my two points are (9, 6) and (12, 0).
The gradient of the line for the final 3 seconds is -2. This means that the acceleration is -2 m/s2. A negative value for acceleration means that the object is slowing down; the object is decelerating. It is fine to say that the object is either accelerating at -2 m/s2 or that the object is decelerating at 2 m/s2.