Question

Chapter 2, #31

You are driving through town at 12 m/s when suddenly a car backs out of a driveway in front of you. You apply the brakes and begin decelerating at 3.3 m/s2. How much time does it take to stop? After braking half the time found in part A, is your speed 6.0 m/s, greater than 6.0 m/s, or less than 6.0 m/s?

Answer 1

We have the kinematic equations

                                    .............................(1)

                                    .....................(2)

                   and               ..................(3)

Where, v is final velocity, u is initial velocity, a is acceleration, S is displacement, x₀ is initial position, and t is time of motion.

A. The car was moving with a velocity of 12 m/s. Given,

                                    u = 12 m/s

                                    a = -3.3 m/s²

                                    v = 0 m/s

Applying equation (1), we get

                                  

                             or,

B. Half time = 3.64/2 = 1.82 s

The speed of the car after 1.82 s of breaking was

                                 

Hence, after braking half the time found in part A, car was moving at 6 m/s.

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