First slide

Power

Question

A body is moving on a frictionless horizontal surface under the influence of a constant force $\vec{F} = (3 \hat{i} + 4 \hat{j}) m / \sec^{2} .$ When the velocity of the body is $(2 \hat{i} - 3 \hat{j}) m$ its kinetic energy.

Moderate

A

is increasing at a rate of 4 Joule / sec.
B

increasing at a rate of 5 Joule/sec.
C

decreasing at a rate of 6 Joule / sec.
D

decreasing at a rate of 4 Joule / sec.

Solution

(3)
$w h e n \vec{v} = (2 \hat{i} - 3 \hat{j}) m / s$ , rate of work done on the body
$\vec{F} . \vec{v} = (3 \hat{i} + 4 \hat{j}) . (2 \hat{i} - 3 \hat{j}) J / s$
$= (6 - 12) J / S = - 6 J / S .$
So by work - energy Theorem, kinetic energy is decreasing at a rate of 6 Joule / sec.

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