First slide

Work Energy Theorem

Question

A particle can move along x-axis initially. The particle is at rest at the origin and force $\vec{F} = 2 t \hat{i} N$ is applied on it. If mass of the particle is 1 kg, the work done by the force in 2 second is

Easy

A

8J
B

16 J
C

12 J
D

48 J

Solution

Acceleration of the particle, $a = \frac{2 t}{1} m / s^{2} = 2 t m / s^{2}$
$\begin{array}{l} ∴ \frac{dv}{dt} = 2 t \Rightarrow \int_{0}^{v} dv = 2 \int_{0}^{t} tdt \Rightarrow v = t^{2} m / s \\ At t = 2 \sec, v = m / s = 4 m / s \\ ∴ By work - energy theorm, W = K_{f} - K_{i} = \frac{1}{2} \times 1 \times 4^{2} - 0 = 8 J \end{array}$

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