The brakes on your automobile are capable of creating acceleration of 14 ft/s2. If you are going 66 mi/hr and suddenly see a state trooper, what is the minimum time required to get your car to 55 mi/hr?

Convert values to consistent units:

66 mi/h = 66 mi/h *5280 ft/mi ÷ 3600 s
= 96.8 ft/s

similarly
55 mi/h = 80.67 ft/s

acceleration = -14 ft/s²

Time required=(80.67-96.8)/(-14)
= 1.15 s

Do not forget to add the reaction time, which could exceed the mechanical deceleration time.

To find the minimum time required to get your car to 55 mi/hr, you'll need to calculate the deceleration required to reduce the speed from 66 mi/hr to 55 mi/hr. The deceleration will be equal to the negative acceleration provided by the brakes.

Step 1: Convert the speeds from miles per hour to feet per second.
1 mile = 5280 feet
1 hour = 3600 seconds

66 mi/hr = (66 * 5280) / 3600 ft/s ≈ 96.53 ft/s
55 mi/hr = (55 * 5280) / 3600 ft/s ≈ 80.67 ft/s

Step 2: Calculate the change in velocity (Δv) by subtracting the final velocity from the initial velocity:

Δv = 80.67 ft/s - 96.53 ft/s = -15.86 ft/s
(Note: The negative sign indicates deceleration)

Step 3: Determine the time required using the equation of motion:

Δv = a * t

Where:
Δv = Change in velocity
a = Acceleration (deceleration in this case)
t = Time

Rearranging the equation to solve for time (t):

t = Δv / a

Substituting the values:

t = (-15.86 ft/s) / (-14 ft/s^2) = 1.13 seconds

Therefore, the minimum time required to get your car from 66 mi/hr to 55 mi/hr is approximately 1.13 seconds.