Question

Spotting a police car, police car you brake a Porsche frem 75 kend to to 45 km/h over displacement of 88 m. @ What is the acceleration, assumed to be constant? 6 What is the elapsed time? @ If you continue to slow down with the acceleration calculated in (a) above, how much time would elapse in bringing the car to rest from 75 km/h? & In (6) above, what distance would be covered? @ Suppose that, on a second trial with the acceleration calculated in (a) above and a different initial velocity, you bring your car to rent after traversing 200m. What was the total braking time ? Windows'u E

Answer 1

a. Initial speed V_i = 75 km/h

= 20.83 m/s

Speed after applying brake V_f = 45 km/h

= 12.5 m/s

From kinematics we have V_f² = V_i² + 2as

or, (12.5)² = (20.83)² + 2a(88)

or, a = [ (12.5)² - (20.83)² ]/ 176

or, a = - 1.58 m/s²

b.Since V_f = V_i + at

or, t = ( 12.5 - 20.83)/ ( - 1.58 )

or, t = 5.27 s

c.  Let ime taken to stop the car from V_I = 20.83 m/s is T s

So, V_f = V_i + aT

or, 0 = 20.83 - 1.58 T

or, T = 20.83/1.58

or, T = 13.18 s

d. From kinematics we have

D = V_iT + 0.5 a T²

or, D = 20.83 (13.18) + 0.5 ( - 1.58)(13.18)²

or, D= 137.31 m

e. Let the initial peed of the car is V_i

From kinematics we can write 0 = V_i² + 2 (-1.58) (200)   

Or, V_i = [ 632]^0.5 m/s

or, V_i = 25.14 m/s

Now let us consider braking time t s

So, 0 = 25.14 - 1.58t

or, t = 25.14/1.58

or, t = 15.91 s