Question

A block of mass of $1kg$ is moving on the x-axis. A force $F$ acting on the block is shown. Velocity of the block at time $t=2s$ is $-3m/s$. What is the speed of the block at time $t=4s$?

• A. $8m/s$
• B. $2m/s$
• C. $3m/s$
• D. $5m/s$

Answer 1

The correct option is C $3m/s$

Given, mass of block $\left(m\right)=1kg$
Velocity of block at time $\left(t\right)2s$ is $-3m/s$
Impulse during $t=2s$ to $t=4s$,

From the graph,
$I=$ Area of $△ABC+$ Area of $△CDE$
$=\frac{1}{2}(3-2)\times 5+\frac{1}{2}(4-3)(-5)$
$=\frac{1}{2}\times 5\times +\frac{1}{2}\times \left(1\right)(-5)$
$=\frac{5}{2}-\frac{5}{2}=0$

We know that,
Impulse $=$ Change in momentum
$0=m{v}_f-m{v}_i$
$\Rightarrow m{v}_f-m{v}_i=0$
$\Rightarrow m{v}_f=m{v}_i$
$v_f=v_i=-3m/s$ or $|3m/s|$.