Question

A car driving on the turnpike accelerates uniformly in the positive x direction from 80 ft/s (54.5 mph) to 103 ft/s (70.2 mph) in 3.10s. What is the x- component of the car's acceleration ? How far does the car travel while it accelerate?

Answer 1

Acceleration = (change in speed) / (time for the change)

Change in speed = (ending speed) - (starting speed)

= (103 fps) - (80 fps) = 23 ft/sec .

Acceleration = (23 ft/sec) / (3.1 sec) = 7.42 ft/sec² .

Since the acceleration was uniform in the x-direction,
its component in the x-direction is 7.42 ft/sec², and it
has no other component.
_________________________________

The car's average speed while it accelerates is

(1/2) (80 fps + 103 fps) = 183/2 = 91.5 fps

In 3.1 seconds, at an average speed of 91.5 fps,
the car travels
(91.5 ft/sec) x (3.1 sec) = 283.65 ft .