A car accelerates uniformly from rest to a
speed of 91.4 mi/h in 7.68 s.
Find the constant acceleration of the car.
Answer in units of m/s
Vf = 91.4mi/h * 1600m/mi * 1h/3600s. = m/s.
a = (Vf-Vo)/t = m/s^2.
Vo = 0.
a = ?
To find the constant acceleration of the car, we can use the following formula:
Acceleration (a) = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 0 (since the car starts from rest)
Final velocity (v) = 91.4 mi/h
Time (t) = 7.68 s
First, let's convert the final velocity from miles per hour to meters per second (since the answer is required in m/s):
1 mile = 1.60934 kilometers
1 kilometer = 1000 meters
1 hour = 3600 seconds
So, 91.4 mi/h = (91.4 * 1.60934 * 1000) meters / (3600 seconds)
Now, we can substitute the values into the formula:
Acceleration (a) = (91.4 * 1.60934 * 1000 meters / 3600 seconds - 0 meters) / 7.68 seconds
Simplifying this expression, we get:
Acceleration (a) = (26193.9736 - 0) meters / 7.68 seconds
Acceleration (a) = 26193.9736 meters / 7.68 seconds
Now, we can divide the numerator by the denominator:
Acceleration (a) = 3410.41 meters / second (rounded to two decimal places)
Therefore, the constant acceleration of the car is approximately 3410.41 m/s.