Question

Figure shows the position-time graph of a particle of mass $4kg$. What is the (a) force on the particle for $t<0,t>4s,0<t<4s$ (b) impulse at t = 0 and t = 4 s? (Consider one-dimensional motion only).

Answer 1

(a) $Force=ma$

$a=\frac{d^{2}x}{d{t}^2}=0$ for straight lines

Hence, $F=0$ for all the regions

(b) Impulse $=F\times t=m(v_2-v_1)$

$v=\frac{dx}{dt}$

For $t<0,v=0$

$0<t<4,v=3/4m/s$

$t>4,v=0$

Impulse at ${}_{t=0}:4\times (\frac{3}{4}-0)=3m/s$

Impulse at ${}_{t=4}:4\times (0-\frac{3}{4})=-3m/s$