-->

Laws Of Motion

Question
CBSEENPH11016606

Force – time curve for a body of mass 7.59 kg is shown in the figure. What is the velocity of the body at the end of 10s? Assume the body starts from rest. 


Solution

Area under Force–time graph is equal to the impulse or change in the momentum of the body. 

Now, Area under F–t graph,
From, t = 0 to t = 10s = Area of trapezium 1+ Area of trapezium 2 + Area of rectangle 3 
        space space space equals left square bracket 1 half left parenthesis 5 plus 12 right parenthesis cross times 4 right square bracket space plus space left square bracket 1 half left parenthesis 12 plus 7 right parenthesis cross times 3 right square bracket plus left square bracket 7 cross times 3 right square bracket 
           = 34 + 28.5 + 21 = 83.5

∴ Change in momentum of body = 83.5 Ns 
i.e.            m(v - 0) = 83.5 
rightwards double arrow            7.59 x v = 83.5 
rightwards double arrow                       v = 11 m/s, is the velocity of the body.