A force F is applied to a cart of mass 10kg initially at rest. The quadratic variation of force with time is shown in the graph. The speed of cart at t=5sec is
A
10m/s
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B
8.33m/s
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C
2m/s
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D
zero
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Solution
The correct option is B8.33m/s Mass of cart =10kg
The equation of force acting on the cart =2t2 [from graph]
Equation of F−t curve (parabolic), F(t)=kt2
Since at t=1 sec,F=2 N⇒k=2 ⇒F(t)=2t2
Acceleration, a(t)=F(t)m a=2t210m/s2 a=t25m/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)=t315m/s ⇒ The speed of cart at t=5sec is v=5315m/s =12515m/s =253m/s v=8.33m/s