Question

A net force $\sum F_x\left(t\right)=A+B{t}^2$ in the +x direction is applied to a girl of mass m. The force starts at t=0 and continues until time t.

• A. Impulse of the force is 2B t
• B. Her speed at time t is $\frac{A}{m}t+\left(\frac{B}{3m}\right)t^3$
• C. Impulse of the force is $At+\left(\frac{B}{3}\right)t^3$
• D. Her speed at time t is $\left(\frac{2B}{m}\right)t$

Answer 1

Answer: (B), (C)

Her speed at time t is $\frac{A}{m}t+\left(\frac{B}{3m}\right)t^3$
Impulse of the force is $At+\left(\frac{B}{3}\right)t^3$

The impulse of the force is given as :

$I=\int Fdt=(A+B{t}^2)dt=At+\frac{B{t}^3}{3}$

Impulse is equal to change in momentum

$I=mv-0\Rightarrow v=\frac{At}{m}+\frac{B{t}^3}{3m}$

Hence B and C are correct options.