Question

A body of mass 0.5 kg travels in a straight line with velocity, v = ax^3/2, where a = 5m ^–1/2/s. What is the work done by the net force during its displacement from x = 0 to x = 2 m?

• A. 50 J
• B. 10 J
• C. 20 J
• D. 30 J

Answer 1

Answer: (A)

Mass of the body (m) = 0.5 kg
Velocity of the body (v) = ax^3/2
where, a = 5m^–1/2/s
Velocity of the body at x = 0,
v₁ = 5 $\times$ 0 = 0
Velocity of the body at c = 2 m
v₂ = 5 $\times$ (2)^3/2m/s
According to work-energy theorem
Work done = Change in K.E.
$=\frac{1}{2}{\text{mv}}_2^2-\frac{1}{2}{\text{mv}}_1^2$
$=\frac{1}{2}m\left({\text{v}}_2^2-{\text{v}}_1^2\right)=\frac{1}{2}\times \text{0.5}\left({\left(5\times 2^{3/2}\right)}^2-0^2\right)$
$=\frac{1}{2}\times \text{0.5}\times 25\times 8$
= 50 J