1: Kinematics

P10_001.m

Two bike riders have their velocities measured as they travel along a straight track. The measurements are plotted in the graph below where at time t = 0 s, the two riders are side by side.

Answer true or false for the following statements when time t = 30 s.

A They are again side by side.

B They have identical accelerations.

C Rider X is travelling faster than rider Y.

D Rider X has travelled further than rider Y.

Justify each answer.

Did any of your answers change after doing the following calculations.

Calculate the following

1. Distance travelled by both riders in 30 s.

2. Maximum acceleration (magnitude) of both riders.

3. Velocity of both riders after 25 s.

4. The time at which bike X stops. What assumption did you need to make?

View solution below only after you have completed the answering the question.

Solution

A FALSE: Area under v / t graph gives the displacement s. So, the area under the graphs for the 30 s time interval are not equal, therefore they have travelled different distances.

B FALSE: The slope of the tangent to the v / t graph equals the velocity. After 30 s, rider Y has zero acceleration and rider X has a negative acceleration.

C FALSE: After 30 s the two riders has identical velocities.

D TRUE: Area under v / t graph gives the displacement s . The area under the v / t graph for rider X is greater than the area for rider Y, hence rider X has a travelled a greater distance.

(1)

Area under v / t graph gives the displacement s.

Rider X area = (10)(20)+(10)(5)+(1/2)(10(5) = 275

Rider Y area = (30)(5) = 150

Distance travelled by rider X is 275 m

Distance travelled by rider Y is 150 m

(2)

The slope of the tangent to the v / t graph equals the acceleration.

Rider Y travels at a constant velocity, so their acceleration is zero.

Rider X travels at a constant velocity, so their acceleration is zero in the time interval from 0 s to 20 s.

Rider X has a negative acceleration in the interval from 20 s to 30 s.