Question

A particle of mass $0.1 \, kg$ is subjected to a force which varies with distance as shown in the figure. If it starts its journey from rest at $x=0$ , its velocity at $x=12 \, m$ is

• A. $0ms^{- 1}$
• B. $40ms^{- 1}$
• C. $20\sqrt{2}\text{m s}^{- 1}$
• D. $20ms^{- 1}$

Answer 1

Answer: (B)

Net work done by the force = area under the curve
$=\frac{4 \times 1 0}{2}+4\times 10+\frac{4 \times 1 0}{2}=80\text{J}$
According to work-energy theorem
ΔK.E. = W_net
$\frac{1}{2} \text{m} \text{v}^{2} - 0 = 8 0 \text{or} \frac{1}{2} \times 0 \cdot 1 \text{v}^{2} = 8 0$
$\text{v}=\sqrt{1 6 0 0}=40\text{m s}^{- 1}$