Question

The driver of a car wishes to pass a truck that is traveling at a constant speed of 20.3 m/s. Initially, the car is also traveling at a speed 20.3 m/s and its front bumper is a distance 24.7 m behind the truck's rear bumper. The car begins accelerating at a constant acceleration 0.650 m/s2, then pulls back into the truck's lane when the rear of the car is a distance 25.5 m ahead of the front of the truck. The car is of length 4.80 m and the truck is of length 21.5 m. A. How much time is required for the car to pass the truck?

B. What distance does the car travel during this time?
C. What is the final speed of the car?

Answer 1

Step-by-step explanation:

Initial relative velocity of the car = 0

relative acceleration = .65 m /s²

relative distance covered = 24.7 + 21.5 + 4.8 + 25.5 = 76.5 m

Let time taken be t

from the relation

s = ut + 1/2 a t²

76.5 = 0 + .65/2 t²

t = 15.34 s

actual distance covered by car during this period

s = ut + 1/2 a t²

= 20.3 x 15.34 + 1/2 x .65 x 15.34²

= 311.4 +76.47

= 387.87

C )

v = u + at

= 20.3 + .65 x 15.34

= 30.27 m /s