A large block that can move along a straight track has a mass of 35.0 kg and an

Question

A large block that can move along a straight track has a mass of 35.0 kg and an initial velocity of 5.00 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 t (s) 10 I 20 30 10- 20 (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 m/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. m/s

Explanation / Answer

a = F/m = 20/35 = 0.5714 m/s2

a) For the 1st 20s, F is opposing the motion. So, a is negative.

Using: v = u + at

=> v = 5 + (-0.5714)(20) = -6.429 m/s

negative sign means the direction of motion has changed.

So the velocity is in the positive x-direction.

Hence, v = +6.429 m/s

b) For the next 10s,

F = 10N alon -x direction

so,

a = -10/35 = -0.2857

v = u + at, ( u is the velocity at 20 s = 6.429m/s)

=> v = (6.429) + (-0.2857)(10) = 3.57 m/s (in the +x direction)

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