In a bumper car arena, two cars of equal mass are heading straight toward each other. The orange car is traveling at a velocity of 5 m/s. The green car is traveling at a velocity of 2 m/s. After the collision, both cars move off in the direction in which the orange car was travelling with a velocity of 1.5 m/s. Which car has the largest change in velocity?

Question

Responses
A green, because its velocity was slowergreen, because its velocity was slower
B green, because it changed directiongreen, because it changed direction
C orange, because it changed directionorange, because it changed direction
D neither, because they both change equally

Answer 1

To determine which car has the largest change in velocity, we will calculate the change in velocity for both cars.

1. Orange Car:

   • Initial velocity (v₀) = 5 m/s (toward the right, let's say)
   • Final velocity (v_f) = 1.5 m/s (after the collision, in the same direction)
   • Change in velocity (Δv) = v_f - v₀ = 1.5 m/s - 5 m/s = -3.5 m/s

2. Green Car:

   • Initial velocity (v₀) = -2 m/s (toward the left, opposite direction to orange)
   • Final velocity (v_f) = 1.5 m/s (after the collision, now in the direction of the orange car)
   • Change in velocity (Δv) = v_f - v₀ = 1.5 m/s - (-2 m/s) = 1.5 m/s + 2 m/s = 3.5 m/s

Now we compare the absolute changes in velocity:

• For the orange car: |Δv| = 3.5 m/s
• For the green car: |Δv| = 3.5 m/s

Both cars have an absolute change in velocity of 3.5 m/s. However, to determine who has the largest change in velocity, we should consider the actual changes:

• The change for the orange car is -3.5 m/s (indicating a decrease in speed).
• The change for the green car is +3.5 m/s (indicating an increase in speed).

Since the green car underwent an increase in velocity while the orange car underwent a decrease in velocity, the green car has the larger overall change in the context of how we interpret "change."

Thus, the correct response is:

A green, because its velocity was slower.