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The brakes on your automobile are capable of creating a deceleration of 17 ft/s", If you are going 85 mi/h and suddenly see a state trooper, what is the minimum time in which you can get your car under the 55 mi/h speed limit?

The brakes on your automobile are capable of creating a deceleration of 17 ft/s", If you are going 85 mi/h and suddenly see a state trooper, what is the minimum time in which you can get your car under the 55 mi/h speed limit?

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
Given:
Initial speed of your car, v0 = 85 mi/h.
Final speed of car, v = 55 mi/h.
Deceleration provided by brakes, a = -17.ft/s2.
The negative sign in the deceleration highlights the fact that the acceleration acts in the direction opposite to the direction of initial velocity.
First, convert the deceleration from ft / s2 to mi/h2 as:
232-2235_6.PNG
Therefore the deceleration provided by the brakes is -41, 727.3 mi/h2.
The time taken by the car to reach the final speed v under the deceleration a, can be calculated using the equation of kinematics as:

232-2148_7.PNG
Therefore the time taken by the car to reach the final speed of 55 mi / h after applying brakes is 2.5 s.

This time is the minimum time the car will take, as the driver continue to apply the brakes, the car will slow down, thereby reducing the final speed. But this would not happen before2.5 s.

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