Question

A Lamborghini sports car can accelerate from zero to 60 mph in 5 seconds. It can decelerate from 60 mph to rest in 140 ft. What is the ratio of average acceleration over average deceleration?

Answer 1

Answer:

0.635

Explanation:

case 1

initial speed of car = 0 mph

final speed of car = 60 mph

time = 5 s

1 mph = 0.44704 m/s

60 mph = 26.8224 m/s

now, acceleration of the car

$a_1 = \dfrac{v_f-v_i}{t}$

$a_1 = \dfrac{26.8224-0}{5}$

    a₁ = 5.36 m/s²

case 2

initial speed = 60 mph = 26.8224 m/s

final speed = 0 m/s

distance = 140 ft

1 ft = 0.3048 m

140 ft = 42.67 m

s = 42.67

using equation of motion

v² = u² + 2 a₂ s

0² = 26.8224² + 2 x a₂ x 42.67

a₂ = - 8.43 m/s²

negative sign is because car is decelerating

a₂ =  8.43 m/s²

now,

$ratio = \dfrac{a_1}{a_2}$

$ratio = \dfrac{5.36}{8.43}$

ratio = 0.635