A car sits in an entrance ramp to a freeway, waiting for a break in the traffic.

Question

A car sits in an entrance ramp to a freeway, waiting for a break in the traffic. The driver sees a small gap between a van and an 18-wheel truck and accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of 21.0 m/s when it reaches the end of the ramp, which has length 121 m.

Part A- What is the acceleration of the car? (units in m/s2)

Part B- How much time does it take the car to travel the length of the ramp? (units in s)

Part C- The traffic on the freeway is moving at a constant speed of 21.0 m/s . What distance does the traffic travel while the car is moving the length of the ramp? (units in m)

Explanation / Answer

Given initial velocity u = 0 m/s

final velocity v = 21 m/s

distance S = 121 m

part A

acceleration a = v^2 / 2s

acceleration a = (21)^2 / 2*121

a = 1.82 m/s^2

part B

time taken t = v/a = 21/1.82 = 11.54 m/s

part C

distance d = speed * time

d = 21 * 11.54

d = 242.3 m

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