A car starts at a position of x=7 m and has a speed of 2 mph. After 85 s the car has a speed of 28 mph. Determine the magnitude of the car's average acceleration during this time.
V1 = 2mi/h * 1600m/mi * 1h/3600s = m/s.
V2 = 28mi/h * 1600m/mi * 1h/3600s = m/s.
a = (V2 - V1)/t = m/s^2.
To determine the magnitude of the car's average acceleration, we need to calculate the change in velocity and divide it by the change in time.
First, let's convert the speeds from mph to m/s since the units need to be consistent. We know that 1 mph is equal to 0.44704 m/s.
The initial speed is 2 mph, so its equivalent in m/s is 2 mph * 0.44704 m/s = 0.89408 m/s.
The final speed is 28 mph, so its equivalent in m/s is 28 mph * 0.44704 m/s = 12.51312 m/s.
Next, we calculate the change in velocity:
Change in velocity = Final velocity - Initial velocity
Change in velocity = 12.51312 m/s - 0.89408 m/s
Change in velocity = 11.61904 m/s
Now, we calculate the change in time. The car's acceleration took place over a time interval of 85 s.
Change in time = 85 s
The average acceleration can now be determined by dividing the change in velocity by the change in time:
Average acceleration = Change in velocity / Change in time
Average acceleration = 11.61904 m/s / 85 s
Average acceleration ≈ 0.136465 m/s²
Therefore, the magnitude of the car's average acceleration during this time is approximately 0.136465 m/s².