First slide

Work

Question

A particle which is experiencing a force given by $\vec{F} = 3 \hat{i} - 12 \hat{j}$ undergoes a displacement of $\vec{d} = 4 \hat{i}$ . If the particle had a kinetic energy of $3 J$ at the beginning of the displacement , what is the kinetic energy at the end of the displacement?

Moderate

Solution

According to work energy theorem
Work done = Change in kinetic energy
$\begin{array}{l} \Rightarrow W = Δ K E \\ \Rightarrow W = K E_{f} - K E_{i} \\ \Rightarrow K E_{f} = W + K E_{i} \\ \Rightarrow K E_{f} = \vec{F} \cdot \vec{S} + K E_{i} \\ \Rightarrow K E_{f} = (3 \hat{i} - 12 \hat{j}) \cdot (4 \hat{i}) + 3 \\ \Rightarrow K E_{f} = 12 + 3 \\ \Rightarrow K E_{f} = 15 J \end{array}$

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