Calculating Distance Traveled and Constant Acceleration of a Car

Understanding the Problem

A car accelerates uniformly from rest to a speed of 40.0 mi/h in 12.0 s. We are tasked to find two values: (a) the distance the car travels during this time and (b) the constant acceleration of the car.

Given Data

Initial Position (Xi): 0m
Initial Velocity (Vi): 0m/s
Final Velocity (Vf): 40m/s
Time (t): 12s

Calculations

Distance Traveled (Xf):

Xf = Xi + 1/2(Vi + Vf)t

Xf = 0 + 1/2(0 + 40)12

Xf = 1/2(40)12

Xf = 240m

Constant Acceleration (a):

Vf = Vi + at

40 = 0 + a(12)

40 = 12a

a = 3.33m/s^2

Results

The car travels a distance of 240 meters during this time, and it accelerates at a constant rate of 3.33 m/s^2.