To determine which car has the largest change in velocity, we need to analyze the initial and final velocities of each car.
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Initial Velocities:
- Orange car: \( v_{o} = 5 , \text{m/s} \) (to the right, let's consider this as positive)
- Green car: \( v_{g} = -2 , \text{m/s} \) (to the left, opposite direction, hence negative)
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Final Velocities:
- After the collision, both cars move in the direction of the orange car with a velocity \( v_{f} = 1.5 , \text{m/s} \).
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Change in Velocity Calculation:
- Change in velocity for the orange car: \[ \Delta v_{o} = v_{f} - v_{o} = 1.5 , \text{m/s} - 5 , \text{m/s} = -3.5 , \text{m/s} \]
- Change in velocity for the green car: \[ \Delta v_{g} = v_{f} - v_{g} = 1.5 , \text{m/s} - (-2 , \text{m/s}) = 1.5 , \text{m/s} + 2 , \text{m/s} = 3.5 , \text{m/s} \]
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Magnitude of Change in Velocity:
- The magnitude of change in velocity for the orange car is \( 3.5 , \text{m/s} \).
- The magnitude of change in velocity for the green car is \( 3.5 , \text{m/s} \).
Since the orange car changes from a positive velocity to a negative change (indicating a change in direction), and the green car has a smaller initial velocity that turns into a larger positive velocity, they both experience the same magnitude of change in velocity.
However, in terms of the velocity change also taking into account the direction, the green car changes from a negative velocity to a positive velocity, indicating a more significant directional change.
So the most appropriate option would be:
B: green, because it changed direction