Question

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

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

Answer 1

Answer: (D)

3 m/s

Answer 2

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

From the graph,
$I=$ Area of $\Delta\, ABC$ + Area of $\Delta \,CDE$
$=\frac{1}{2}(3-2) \times 5+\frac{1}{2}(4-3)(-5)$
$=\frac{1}{2} \times 1 \times 5+\frac{1}{2} \times(1)(-5)$
$=\frac{5}{2}-\frac{5}{2}=0$
We know that,
Impulse = Change in momentum
$0 =m v_{f}-m v_{i}$
$\Rightarrow \, m v_{f}-m V_{i} =0$
$\Rightarrow \,m V_{f} =m v_{i}$
$V_{f} =v_{i}=-3 \,m / s$
or $|3 \,m / s |$