A car in stop-and-go traffic starts at rest, moves forward 13 m in 8.0 s, then comes to rest again. The velocity-versus-time plot for this car is given in Figure 30. What distance does the car cover in (a) the first 4.0 seconds of its motion and (b) the last 2.0 seconds of its motion? (c) What is the constant speed V that characterizes the middle portion of its motion?

FIGURE 30

Solution 66P

Step 1 of 4:

Calculate the distance travelled by the car in first 4.0 s.

Then calculate the distance travelled by car in last 2.0 s.

And calculate the maximum velocity .

(a)

Step 2 of 4:

Consider the final maximum velocity of the car is .

In first 4.0 second the car is moving with constant velocity starting from rest and the maximum velocity is . Hence the distance travelled in this 4 second is

Now, for next 2.0 s, the car is moving with constant velocity , hence, the distance travelled in this two second is

Then, for next two second, the car is moving with constant deceleration and stops. Hence distance travelled in this two second is

Hence, the total distance travelled is

So,

Hence, distance travelled by the car in first 4.0 second is 5.2 m.

(b)