A car starts at a position of x=5 m and has a speed of 6 mph. After 32 s the car has a speed of 25 mph. Determine the magnitude of the car's average acceleration during this time
6 mph = 8.8 ft/s
25 mph = 36.7 ft/s
Avg. Acceleration = (velocity change)/time
= 27.9/32 = 0.87 ft/s^2 = 0.027 g's
That is quite slow acceleration for a car.
To calculate the magnitude of the car's average acceleration, we first need to determine its change in velocity and the time interval.
Given:
Initial position, x1 = 5 m
Initial speed, v1 = 6 mph
Final speed, v2 = 25 mph
Time interval, t = 32 s
We need to convert the speeds from mph (miles per hour) to m/s (meters per second) since the unit of acceleration is typically expressed in m/s².
Step 1: Convert the initial and final speeds to m/s.
1 mph is approximately equal to 0.44704 m/s.
Initial speed, v1 = 6 mph = 6 * 0.44704 m/s = 2.68224 m/s
Final speed, v2 = 25 mph = 25 * 0.44704 m/s ≈ 11.176 m/s
Step 2: Calculate the change in velocity.
Change in velocity, ∆v = v2 - v1 = 11.176 m/s - 2.68224 m/s ≈ 8.49376 m/s
Step 3: Calculate the magnitude of the average acceleration.
Average acceleration, a = ∆v / t
Substituting the values:
a = (8.49376 m/s) / (32 s) ≈ 0.2654 m/s²
Therefore, the magnitude of the car's average acceleration during this time is approximately 0.2654 m/s².