Question

A car traveling 57.0 km/h is 27.9 m from a barrier when the driver slams on the brakes. The car hits the barrier 2.64 s later. (a) What is the car's constant deceleration magnitude before impact? (b) How fast is the car traveling at impact? (a) Number-5.69 (b) NumberTT-0.9416 UnitsT m/s 2 UnitsT m/s

Answer 1

1 km = 1000 m

1 hour = 3600 sec

Initial velocity of the car = V₁ = 57 km/hr = 57 x (1000/3600) m/s = 15.833 m/s

Initial distance between the car and the barrier = D = 27.9 m

Acceleration of the car = a

Time taken by the car to hit the barrier = T = 2.64 sec

D = V₁T + aT²/2

27.9 = (15.833)(2.64) + a(2.64)²/2

a = -3.988 m/s²

Negative as it is deceleration.

Velocity of the car when it hits the barrier = V₂

V₂ = V₁ + aT

V₂ = 15.833 + (-3.988)(2.64)

V₂ = 5.305 m/s

We are asked for the magnitude of the car's deceleration therefore it will be positive.

a) Magnitude of the car's deceleration before the impact = 3.988 m/s²

b) Speed of the car at impact = 5.305 m/s