Question

The kinetic energy of a particle varies with time as k =
(3t2 – 2t + 1) J, where t is in second. The power applied
on the particle at t = 1s is
4 watt
8 watt
6 watt
2 watt​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The kinetic energy of a particle varies with time as

$\sf{k = (3 {t}^{2} - 2t + 1) \: \: J }$

where t is in second. The power applied

on the particle at t = 1 s is

• 4 watt

• 8 watt

• 6 watt

• 2 watt

EVALUATION

We are aware of the formula that if k is the kinetic energy and P is the Power applied then

$\displaystyle \sf{P = \frac{dk}{dt} }$

Here it is given that

$\sf{k = 3 {t}^{2} - 2t + 1 }$

Differentiating both sides with respect to t we get

$\displaystyle \sf{ \frac{dk}{dt} = 6t - 2}$

$\displaystyle \sf{ \therefore \: P = 6t - 2 }$

∴ The power applied on the particle at t = 1

$= \sf{P_{t = 1}}$

$= (6 \times 1) - 2$

$= 6 - 2$

$= 4$

FINAL ANSWER

Hence the correct option is 4 watt

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