Calculate the force needed to bring a 950-kg car to rest from a speed of 90.0 km/h in a distance of 120 m (a fairly typical distance for a non-panic stop). (b) suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.00 m.

a)

2474 N

b)

148438 N

Explanation:

(a)

v₀ = initial velocity of the car = 90 km/h = 25 m/s

v = final velocity of the car = 0 m/s

d = stopping distance for the car = 120 m

F = force needed to bring the car to rest

m = mass of the car = 950 kg

Using Work-change in kinetic energy theorem

F d Cos180 = (0.5) m (v² - v₀²)

F (120) (-1) = (0.5) (950) (0² - 25²)

F = 2474 N

b)

v₀ = initial velocity of the car = 90 km/h = 25 m/s

v = final velocity of the car = 0 m/s

d = stopping distance for the car = 2 m

F = force needed to bring the car to rest

m = mass of the car = 950 kg

Using Work-change in kinetic energy theorem

F d Cos180 = (0.5) m (v² - v₀²)

F (2) (-1) = (0.5) (950) (0² - 25²)

F = 148438 N

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