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Question

A force F is applied to a cart of mass 10 kg initially at rest. The quadratic variation of force with time is shown in the graph. The speed of cart at t=5 sec is

  1. 10 m/s
  2. 8.33 m/s
  3. 2 m/s
  4. zero


Solution

The correct option is B 8.33 m/s
Mass of cart =10 kg
The equation of force acting on the cart =2t2 [from graph]
Equation of Ft curve (parabolic), F(t)=kt2
Since at t=1 sec, F=2 Nk=2
F(t)=2t2
Acceleration, a(t)=F(t)m
a=2t210 m/s2
a=t25 m/s2
Since acceleration, a=dvdt
v(t)=a(t)dt
v(t)=t25dt
v(t)=t315+C
As the cart is initially stationary
v(0)=0
C=0
v(t)=t315 m/s
The speed of cart at t=5 sec is
v=5315 m/s
=12515 m/s
=253 m/s
v=8.33 m/s

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