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 = 0 s and t = 4 s .

Explanation

Given , mass of the body (m) = 2kg
From the position- time graph , the body is at x = 0 when t = 0 i.e., body is at rest .
`therefore` impulse at t = 0 , s = 0 is zero
From t = 0 s to t = 4 s , the position-time graph is a straight line , which shows that body moves with uniform velocity.
Beyond t = 4s , the graph is a straight line parallel to time axis , i.e., body is at rest (v=0).
Velocity of the body = slope of position-time graph
= tan `theta = (3)/(4)` m/s
Impulse (at t = 4 s) = change in momentum
= mv-mu
= m(v-u)
= `2(0 - (3)/(4))`
= `-(3)/(2) kg-m//s = -1.5 ` kg-m/s