Plot the velocity vs. time and the position vs. time for a car that travels at 20 m/s for 20 seconds, then accelerates in 10 seconds to 30 m/s, travels at this speed for 20 seconds, and the brakes and comes to rest in 10 s.

The position-time graph and the velocity-time graph has been shown in the figure attached.

Explanation:

Given:

For t = 0 s to t = 20 s,

The car moves with a constant velocity whose position-time and the velocity time graph has been shown with a red line.

For t = 20 s to t = 30 s,

The car moves with a constant acceleration whose position-time and the velocity time graph has been shown with a green line.

For t = 30 s to t = 50 s,

The car moves with a constant velocity whose position-time and the velocity time graph has been shown with a blue line.

For t = 50 s to t = 60 s,

The car moves with a constant deceleration whose position-time and the velocity time graph has been shown with a black line.

For a constant velocity, the velocity-time graph of the particle is a straight line parallel to a time axis and the position-time graph is a straight line inclined at some positive angle with the time axis.

For a constant acceleration, the velocity-time graph is a straight line incline at a positive angle with the time axis and the position-time graph is a parabolic curved line having upward concavity.  

For a constant deceleration, the velocity-time graph is a straight line incline at a negative angle with the time axis and the position-time graph is a parabolic curved line having downward concavity.

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