A car starts at a position of x=6 km and has a speed of 6 mph. After 42 s the car has a speed of 60 mph. Determine the magnitude of the car's average acceleration during this time.

acceleration=(vf-vi)/time

acceleration=64mph/42 seconds=1.54mph/second

To determine the magnitude of the car's average acceleration during this time, we can use the formula:

Average acceleration (a) = (final velocity - initial velocity) / time

First, let's convert the speeds from mph to km/h, since the initial position is given in kilometers.

6 mph = 9.7 km/h
60 mph = 96.6 km/h

Now, let's convert the time from seconds to hours, since the speeds are given in km/h.

42 s = 0.0117 hours

Now we can calculate the average acceleration:

Average acceleration (a) = (96.6 km/h - 9.7 km/h) / 0.0117 hours
= 86.9 km/h / 0.0117 hours
≈ 7435.9 km/h²

Therefore, the magnitude of the car's average acceleration during this time is approximately 7435.9 km/h².