Question

the momentum initial of the truck is 0
the momentum final of the truck is 75
the change in momentum of the truck is 75
the momentum initial of the car is 0
the momentum final of the car is 25
the change in momentum of the toy car is 25
the has the greatest change in momentum
truck - because it has a larger mass but same change in velocity as the toy car
car - because it has a smaller mass but the same change in velocity as the toy truck
both have the same change in momentum because they both have the same change in velocity
neither - both have a constant momentum

Explanation:

Step1: Recall the momentum formula

Momentum \(p = mv\).

Step2: Analyze the change in momentum for the truck

For the toy - truck, \(m = 15\space kg\), \(v_{i}=0\space m/s\), \(v_{f}=5\space m/s\).
Initial momentum \(p_{i - truck}=m\times v_{i}=15\times0 = 0\space kg\cdot m/s\).
Final momentum \(p_{f - truck}=m\times v_{f}=15\times5=75\space kg\cdot m/s\).
Change in momentum \(\Delta p_{truck}=p_{f - truck}-p_{i - truck}=75 - 0=75\space kg\cdot m/s\).

Step3: Analyze the change in momentum for the car

For the toy - car, \(m = 5\space kg\), \(v_{i}=0\space m/s\), \(v_{f}=5\space m/s\).
Initial momentum \(p_{i - car}=m\times v_{i}=5\times0 = 0\space kg\cdot m/s\).
Final momentum \(p_{f - car}=m\times v_{f}=5\times5 = 25\space kg\cdot m/s\).
Change in momentum \(\Delta p_{car}=p_{f - car}-p_{i - car}=25-0 = 25\space kg\cdot m/s\).

Since \(75>25\), the truck has a greater change in momentum because, using the formula \(\Delta p=m\Delta v\) (where \(\Delta v=v_{f}-v_{i}\) and \(\Delta v_{truck}=\Delta v_{car} = 5 - 0=5\space m/s\)), and \(m_{truck}>m_{car}\)

Answer:

Truck - because it has a larger mass but same change in velocity as the toy car.