Question

The driver 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 20.0 m/s when it reaches the end of the 125 m long ramp.

1.What is the acceleration of the car?
2.How much time does it take the car to travel the length of the ramp?

Answer 1

The car accelerates with a constant acceleration of 1.6 m/s^2 and it takes 12.5 seconds to travel the length of the 125 m ramp.

Step-by-step explanation:

Calculating the Car's Acceleration and Time to Travel the Ramp

To calculate the acceleration of the car, we can use the kinematic equation v^2 = u^2 + 2as, where 'v' is the final velocity, 'u' is the initial velocity, 'a' is the acceleration, and 's' is the displacement. Since the car starts from rest, u = 0, and we are given v = 20.0 m/s and s = 125 m.

v^2 = u^2 + 2as
20^2 = 0 + 2a(125)
400 = 250a
a = 400/250 = 1.6 m/s^2

The acceleration of the car is 1.6 m/s^2.

To calculate the time it takes for the car to travel the length of the ramp, we use the equation v = u + at. Using the calculated acceleration:

v = u + at
20 = 0 + 1.6t
t = 20/1.6 = 12.5 s

The time it takes for the car to travel the length of the ramp is 12.5 seconds.