Determining Acceleration of a Car from Rest

What is the acceleration of a car that starts from rest and accelerates uniformly?

A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car in m/s^2.

Answer:

The acceleration of the car is 8.10 m/s^2.

When a car starts from rest and accelerates uniformly over a certain time and distance, we can calculate the acceleration using the following formula:

x = v_i t + (1/2) a t^2

Where:

v_i is the initial velocity (in this case, 0 m/s as the car starts from rest)

a is the acceleration we want to calculate

t is the time taken (5.21 seconds)

x is the distance traveled (110 m)

Explanation:

Let's substitute the given values into the formula:

Initial velocity (v_i) = 0 m/s (as the car starts from rest)

Time (t) = 5.21 seconds

Distance (x) = 110 m

Substitute these values into the formula:

110m = (0)(5.21s) + (1/2)(a)(5.21s)^2

110m = 0 + (1/2)(a)(5.21s)^2

110m = 13.57s^2 * a

Divide both sides by 13.57s^2:

110m / 13.57s^2 = 13.57s^2 * a / 13.57s^2

8.10 m/s^2 = a

Therefore, the acceleration of the car is 8.10 m/s^2. I hope this explanation helps you understand how to solve for acceleration in a uniform motion scenario.