Question

Force-time$\left(\text{F - t}\right)$ graph of a rocket of mass 1000 kg shown below describes the force on the rocket. Neglecting gravity, the velocity of rocket $16\text{s}$ after starting from rest is

• A. $100\text{m/s}$
• B. $150\text{m/s}$
• C. $200\text{m/s}$
• D. $250\text{m/s}$

Answer 1

The correct option is C $200\text{m/s}$

Given:
Velocity of rocket at $(t=0)$; $v_i=0$
Let Velocity of rocket at $(t=16\text{s})$ is $v_f$.
Using Impulse$\left(J\right)$ = change in momentum $\left(\Delta P\right)$

As we know area under (F -t) graph gives change in momentum.

$\therefore$ we have, $m(v_f-v_i)=$ Area under (F - t) graph from $t=0\text{to}t=16\text{s}$
$\Rightarrow m{v}_f=(\frac{1}{2}\times 4\times 20+4\times 20+\frac{1}{2}\times 8\times 20)\text{kN-s}$
$\Rightarrow 1000v_f=(\frac{1}{2}\times 4\times 20+4\times 20+\frac{1}{2}\times 8\times 20)\times {10}^3\text{N-s}$
$\Rightarrow v_f=200\text{m/s}$