Figure \(\mathrm{P} 4.67\) is a momentum-versus-time graph for a collision between two carts. Carts 1 and 2 have inertias of \(1.0 \mathrm{~kg}\) and \(3.0 \mathrm{~kg}\), respectively. What are the \(x\) components of the initial and final velocities of 

(a) cart 1 and

(b) cart 2?

(c) What are the momentum changes \(\Delta \vec{p}_{1}\) and \(\Delta \vec{p}_{2}\) ?

(d) Do the values you calculated in part \(c\) satisfy Eq. 4.18, \(\Delta \vec{p}=\vec{j}\) ?

(e) Draw the velocity-versus-time graph for this collision. (Hint: You can do this by making some simple changes to Figure P4.67.)

Data from Figure P4.67

Data from Eq. 4.18

P. (kg-m/s) 3 collision 2 cart 1 1 cart 2 cart 1 0 (s) 2 4 6 8 10 cart 2 -1