Question

The figure shows the position-time ($x-t$) graph of one-dimensional motion of a body of mass $0.4kg$. The magnitude of each impulse (in

$Ns$)

is

• A. $0.2$
  
• B. $0.4$
  
• C. $0.6$
  
• D. $0.8$
  

Answer 1

Answer: (D)

Step 1: Given that:

The position-time (x-t) graph of one-dimensional motion of a body of mass($m$) = $0.4kg$

Step 2: Calculation of impulse:

The slope of the position-time graph gives the velocity of the body.

From the graph;

It is seen that

Slope of part OA= Slope of part PC = Slope of part QE = Slope of part RG

Thus, the velocity during these parts = $\frac{AB}{OB}$

= $\frac{2m}{2s}$

u= $1m{s}^{-1}$

The slope of part AP = The slope of part CQ =The slope of part ER =The slope of part GS

The velocity during these parts = $\frac{AP}{BP}$

= $\frac{0m-2m}{4sec-2sec}=\frac{-2}{2}$

v = $-1m{s}^{-1}$

We know that;

Impulse = Change in momentum

Thus,

Impulse in each part = $\text{mv- mu}$

= $0.4kg\times (-1m{s}^{-1})-0.4kg\times (+1m{s}^{-1})$

= $-0.4-0.4$

= $-0.8$

Thus,

Impulse in each part will be $0.8Ns$ .

Hence

Option C) 0.8 is the correct option.