Please help with all parts! thank you!! A cart that can move along a straight tr

Question

Please help with all parts! thank you!!

A cart that can move along a straight track has a mass of 2.00 kg and an initial velocity of 4.00 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 eventually switches direction to the negative x-direction, as shown in the graph of force as a function of time below. The force is directed only in the +x or -x direction. Complete the table below to show the cart's momentum and velocity at the indicated times. Use + and - signs, as appropriate. The cart's momentum at r = 20 s is exactly the same as its momentum at t =

Explanation / Answer

from the graph

we know that the force = change in momentum = m dV = m(v2-v1)

mass of cart m = 2 kg, moving with initial velocity in the -ve x directionwith v0 = 4 m/s

here area under the curve gives the change in momentum

t= 0 s the momentum is p =m*v = 2*(-4) = -8 kg m/s, velocity is v0=-4 m/s

t= 20 s

area under the curve till t= 10 s is = area of rectangle + area of right angle triangle

                   = 20*5+0.5*5*20 = 150 m2

now change in momentum is dP = m (v2-v0)= 150

               2(v2-(-4))= 150 = 71 m/s

              
and area under the curve from t= 10 s to t= 20 s is

   Area = 0.5*10*10 = 100 = m(v3-v2)

           ==> 100 = 2(v3-71), v2 = 121 m/s

momentum P = 100 kg m/s

t = 25 s

   there is no change in momentum and velocity that is

continue with momentum and velocity is p = 100 kg m/s, v4 = 121 m/s

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