Everything Science Grade 10

21.6 CHAPTER 21. MOTION IN ONE DIMENSION

Example 5: Velocity from a position vs. time graph

QUESTION

The position vs. time graph below describes the motion of an athlete.

0

1

2

3

4

0 1 2 3 4 5 6 7

~x(m)

t(s)

1. What is the velocity of the athlete during the first 4 seconds?

2. What is the velocity of the athlete fromt= 4s tot= 7s?

SOLUTION

Step 1:The velocity during the first 4 seconds

The velocity is given by the gradient of a position vs. time graph. During

the first 4 seconds, this is

~v = ∆∆~xt

=^44 ms−−^00 sm

= 1m·s−^1

Step 2:The velocity during the last 3 seconds

For the last 3 seconds we can see that the displacement stays constant.

The graph shows a horizontal line and therefore the gradient is zero.

Thusv= 0 m·s−^1.

422 Physics: Mechanics