Everything Science Grade 10

21.6 CHAPTER 21. MOTION IN ONE DIMENSION

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0 1 2 3 4 5 6

~x(m)

t(s)

SOLUTION

Step 1:Identify what information is given and what is asked for

The question gives a position vs. time graph and the following three

things are required:

1. Draw avvs.tgraph.

2. Draw anavs.tgraph.

3. Describe the motion of the car.

To answer these questions, break the motion up into three sections: 0 –

2 seconds, 2 – 4 seconds and 4 – 6 seconds.

Step 2:Velocity vs. time graph for 0 – 2 seconds

For the first 2 seconds we can see that the position (and hence the

displacement) remains constant - so the object is not moving, thus it has

zero velocity during this time. We can reach this conclusion by another

path too: remember that the gradient of a displacement vs. time graph

is the velocity. For the first 2 seconds we can see that the displacement

vs. time graph is a horizontal line, i.e.. it has a gradient of zero. Thus

the velocity during this time is zero and the object is stationary.

Step 3:Velocity vs. time graph for 2 – 4 seconds

For the next 2 seconds, displacement is increasing with time so the

object is moving. Looking at the gradient of the displacement graph

we can see that it is not constant. In fact, the slope is getting steeper

(the gradient is increasing) as time goes on. Thus, remembering that the

gradient of a displacement vs. time graph is the velocity, the velocity

must be increasing with time during this phase.

Step 4:Velocity vs. time graph for 4 – 6 seconds

For the final 2 seconds we see that displacement is still increasing with

time, but this time the gradient is constant, so we know that the object

418 Physics: Mechanics