A large block that can move along a straight track has a mass of 60.0 kg and an

Question

A large block that can move along a straight track has a mass of 60.0 kg and an initial velocity of 3.20 m/s in the negative x-direction. The cart is then subjected to a net force that is initially in the positive x-direction, but which then switches direction to the negative x-direction at t = 20 s, as shown in the graph below. Fnet N) +30 +20 +10 0- -10 -20 t (s) 10 5 20 25 30 (a) Find the velocity of the cart at t = 20 s. Don't forget to use a minus sign, if the velocity is in the negative direction 9.867 Xm/s (b) Find the velocity of the cart at t30 s. Don't forget to use a minus sign, if the velocity is in the negative direction 2 x m/s

Explanation / Answer

mass m = 60 kg

initial velocity vox = -3.2 m/s

force acting during the time t = 20 s , F = 20 N

impulse J = F*t

impulse momentum theorem

impulse = change in momentum

J = m*(vf - vi)

F*t = m*(vf - vi)

20*20 = 60*(vf - (-3.2))

velocity vf = +3.47 m/s   <<<-----ANSWER

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part (b)

from time t = 20s to t = 30s

the force acting Fx = -10 N

velocity at t1 = 20 s is v20 = 3.47 m/s <<<----------ANSWER

impulse = change in momentum

J = dP

Fx*(30-20) = m*(V30 -v20)

-20*(30-20) = 60*(v30 - 3.47)

velocity at t = 30s , v30 = 0.137 m/s <<<<<----------ANSWER

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