If the driver of a car wishes to increase his speed from 20 mph to 50 mph while traveling a distance of 528 ft., what constant acceleration should he maintain?

To find the constant acceleration required for the driver to increase his speed from 20 mph to 50 mph while traveling a distance of 528 ft, we can use the basic equation of motion:

v² = u² + 2as

Where:
v = final velocity (50 mph)
u = initial velocity (20 mph)
a = acceleration (unknown)
s = distance (528 ft)

First, let's convert the velocities from mph to ft/s, as we need to use consistent units. 1 mph is equal to 1.47 ft/s, so:

Initial velocity (20 mph) = 20 * 1.47 = 29.4 ft/s
Final velocity (50 mph) = 50 * 1.47 = 73.5 ft/s

Now, let's substitute the values into the equation:

73.5² = 29.4² + 2a * 528

Simplifying the equation:
5402.25 = 864.36 + 1056a

Rearranging the equation:
1056a = 5402.25 - 864.36

1056a = 4537.89

Divide both sides by 1056:
a = 4537.89 / 1056

a ≈ 4.30 ft/s²

Therefore, the driver should maintain a constant acceleration of approximately 4.30 ft/s² to increase his speed from 20 mph to 50 mph while traveling a distance of 528 ft.