A 1,000-kg vehicle traveling 4 m/s eastward collided with another vehicle, at which point it moved 1 m/s westward.

Question

A 1,000-kg vehicle traveling 4 m/s eastward collided with another vehicle, at which point it moved 1 m/s westward.

What was the vehicle's change in momentum?

A. 1,000 kg • m/s

B. 3,000 kg • m/s

C. 4,000 kg • m/s

D. 5,000 kg • m/s

I think the answer is either B or C

Answer 1

A 1,000-kg vehicle traveling 4 m/s eastward collided with another vehicle, at which point it moved 1 m/s westward. What was the vehicle's change in momentum?

(A) 1,000 kg • m/s (B) 3,000 kg • m/s (C) 4,000 kg • m/s (D) 5,000 kg • m/s

Detailed Solution:

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Change in momentum of an object is its mass times the change in its velocity. Δp = m⋅(Δv) = m⋅(v_f − v_i)

Given - Mass: m = 1,000-kg, Initial Velocity: v_i = -4 m/s (eastward), Final Velocity: v_f = 1 m/s (westward)

Vehicle's change in momentum:

Δp = m⋅(Δv) = m⋅(v_f − v_i) = 1000⋅(1 − (-4)) = 1000⋅(1 + 4) = 1000⋅(5) = 5,000 kg • m/s <== (D)

Answer 2

Hi.

We just need to multiply the object's change in velocity by its mass. We're going to have to consider the directional change in the velocity (remember that velocity is a vector).

Since the car was going 4 m/s west and then ended up going 1 m/s east, the change in the velocity's magnitude is 5 m/s.

5 m/s x 1,000 kg = 5,000 kg * m/s

The object's change in momentum is 5,000 kg * m/s. That's answer D.