First slide

Work

Question

The displacement of a particle of mass 2kg varies with time as $S = (2 t^{2} - 2 t + 10) m$ . The change in kinetic energy of the particle in a time interval t=0 to t=2s is

Moderate

A

12J
B

16J
C

24J
D

32J

Solution

$\begin{array}{l} W = ΔK . E \\ \int \vec{F} \cdot \vec{d s} = ΔK . E \\ s = 2 t^{2} - 2 t + 10 \Rightarrow d s = (4 t - 2) dt \\ v = 4 t - 2 \Rightarrow a = \frac{d v}{d t} = 4 {ms}^{- 2} \\ \int m a d s = ΔKE \\ 8 \times [[4 \times \frac{t^{2}}{2}] - [2 t]_{0}^{2}] = ΔK . E \\ ΔK . E = 8 [8 - 4] = 32 J \end{array}$

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