Ncert Exercises & Solutions

The position-time graph of a body of mass $2$ kg is as given in the figure. What is the impulse on the body at $t= 0$ s and $t=4$ s.

1.	$1.5~\text{kg-m/s}$
2.	$-1.5~\text{kg-m/s}$
3.	$0.67~\text{kg-m/s}$
4.	$-0.67~\text{kg-m/s}$

Hint: Impulse is equal to change in momentum.

Step 1: Find impulse at t = 0 sec

Given, the mass of the body (m) = 2 kg
From the position-time graph, the body is at x = 0 when t = 0. i.e., body is at rest

$∴$ Impulse at t = 0 s, is zero

Step 2: Find impulse on the body at t = 4 sec
From t = O s to t = 4 s, the position-time graph is a straight line, in which that body moves with uniform velocity.

Beyond t = 4s, the graph is a straight line parallel to the time axis i.e., the body is at rest (v = 0).
The velocity of the body = slope of the position-time graph

$= \tan θ = \frac{3}{4} m / s$

Impulse (at t = 4s) = change in momentum

$\begin{array}{l} = mv - mu \\ = m (v - u) \\ = 2 (0 - \frac{3}{4}) \\ = - \frac{3}{2} kg m / s = - 1 .5 kg m / s . \end{array}$

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