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.