Question

A car is stopped for a traffic signal. When the light turns green,
the car accelerates, increasing its speed from 0 to 5.20 m/s in
0.832 s. What are the magnitudes of (a) the linear impulse and
(b) the average total force experienced by a 70.0-kg passenger
in the car during the time the car accelerates?

Answer 1

Answer:

Impulse, p = 364 N·s
Force F =  437.5 N

Explanation:

First some definitions:

• Momentum, p is defined as the product of the mass, m  and velocity v.
  p = mv
  

• Impulse, J is the change in momentum of a body
  J = Δp = p₂ - p₁ = mv₂ - mv₁ = mΔv   where the subscript 1 refers to initial values and subscript 2 to final values.

Part (a)
Since the car is initially at rest, its initial momentum is 0.
When the car reaches a velocity of 5.20 m/s, the momentum experienced by a 70 kg passenger is

Δv = 5.20 - 0 = 5.20 m/s

p = 70 kg x 5.20 m/s =  50.3248 kg m/s =  364 N·s

p = 384 N.s

Part (b)

Force is given by F=m(Δv/Δt) = 70 kg x (5.20 m/s / 0.832 s) = 437.5 N
F = 437.5 N