Question

Hello,I am trying to find the rate of each segment for this velocity time graph.

Answer 1

The rate of change of a segment in a velocity time graph is the acceleration of the object, which is given by the equation:

`a=(v_f-v_0)/(t_f-t_0)`

First segment.

In this segment the final and initial velocities are 10 and zero, repectively and the final and initial time are 10 and zero, respectively. Plugging these values we have:

`a=(10-0)/(10-0)=1`

Therefore, the rate of change of the first segment (the acceleration) is 1 meters per second per second.

Second segment.

In this segment the final and initial velocities are 10 and 10, respectively. The initial and final time are 10 and 20 seconds, respectively; then we have:

`a=(10-10)/(20-10)=0`

Therefore, the acceleration in this segment is 0 meters per second per second.

Note: An horizontal segment is rate of change is always zero.

Third segment.

In this segment the final and initial velocities are -10 and 10, repectively and the final and initial time are 20 and 30, respectively. Plugging these values we have:

`a=(-10-10)/(30-20)=-(20)/(10)=-2`

Therefore, the rate of change of the third segment (the acceleration) is -2 meters per second per second.

Fourth segment.

In this segment the final and initial velocities are 0 and -10, repectively and the final and initial time are 40 and 30, respectively. Plugging these values we have:

`a=(0-(-10))/(40-30)=(10)/(10)=1`

Therefore, the rate of change of the fourth segment (the acceleration) is 1 meters per second per second.