The sketch of a velocity time graph for the motion of the car which starts from the rest and attains a velocity of 40 in 20 seconds.It maintains this velocity for 30 seconds and then comes to rest in 25 seconds

To sketch a velocity-time graph for the given scenario, we'll follow a step-by-step approach:

Step 1: Identify the time intervals and associated velocities.
- The car starts from rest, so its initial velocity is 0 m/s.
- It attains a velocity of 40 m/s in 20 seconds.
- It maintains this velocity of 40 m/s for 30 seconds.
- It then comes to rest, so its final velocity is 0 m/s, which occurs at 75 seconds (20 + 30 + 25 = 75).

Step 2: Plot the points on the graph.
- The first point should have a time of 0 seconds and a velocity of 0 m/s.
- The second point with a time of 20 seconds and a velocity of 40 m/s.
- The third point with a time of 50 seconds and a velocity of 40 m/s.
- The fourth point with a time of 75 seconds and a velocity of 0 m/s.

Step 3: Connect the points on the graph.
- Starting from the first point, draw a straight line segment to the second point.
- From the second point, continue a straight horizontal line to the third point.
- Finally, draw a straight line segment from the third point to the fourth point.

The resulting graph should be a diagonal line segment rising from the origin (0,0) to (20,40), followed by a horizontal line segment extending from (20,40) to (50,40), and finally, a diagonal line segment descending from (50,40) to (75,0).