(Solved): The \( 10-\mathrm{kg} \) cart with ideal rollers is subjected to the time-varying force \( P \) as ...

The \( 10-\mathrm{kg} \) cart with ideal rollers is subjected to the time-varying force \( P \) as shown in the graph. Note that the force is zero after \( t=5 \mathrm{~s} \). If the velocity of the cart is \( v_{1}=2 \mathrm{~m} / \mathrm{s} \) down the incline at time \( t=0 \), determine its velocity at time \( t=7 \mathrm{~s} \). Assume that the distance between \( A \) and \( B \) is sufficiently large such that mechanical interference does not occur. (1) \( 11.77 \mathrm{~m} / \mathrm{s} \) down the incline (2) \( 7.77 \mathrm{~m} / \mathrm{s} \) down the incline (3) \( 4.23 \mathrm{~m} / \mathrm{s} \) up the incline (4) \( 3.77 \mathrm{~m} / \mathrm{s} \) down the incline (5) \( 31.7 \mathrm{~m} / \mathrm{s} \) up the incline (6) \( 1.258 \mathrm{~m} / \mathrm{s} \) down the incline (7) \( 44.3 \mathrm{~m} / \mathrm{s} \) down the incline (8) None of the above