The position-time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at t = 4 s?

Question

The position-time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at t = 4 s? (A) (2/3)kg m s-1 (B) -(2/3)kg m s-1 (C) (3/2)kg m s-1 (D) -(3/2)kg m s-1

Tardigrade Admin · Accepted Answer

At t = 4 s, the body has constant velocity u=(3/4)m s-1. After t = 4 s, the body is at rest i.e., upsilon =0 ∴ Impulse =m( upsilon-u) =2 kg(0-(3/4)m s-1)=-(3/2)kg m s-1

Q. The position-time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at $t = 4 s$ ?

$\frac{2}{3} k g m s^{- 1}$

$- \frac{2}{3} k g m s^{- 1}$

$\frac{3}{2} k g m s^{- 1}$

$- \frac{3}{2} k g m s^{- 1}$

At $t = 4 s$ , the body has constant velocity
$u = \frac{3}{4} m s^{- 1.}$
After $t = 4 s$ , the body is at rest i.e., $υ = 0$
$∴$ Impulse $= m (υ - u)$
$= 2 k g (0 - \frac{3}{4} m s^{- 1}) = - \frac{3}{2} k g m s^{- 1}$

Q. The position-time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at t=4s?

32​kgms−1

−32​kgms−1

23​kgms−1

−23​kgms−1