A body of mass 1 kg begins to move under the action of a time dependent force F-2t-3t2-N- where - and - are unit vectors along x and y axis- What power will be developed by the force at the time t-

The correct option is D (2t^3+3t^5)W Applying Newton's second #160;law of motion, acceleration, a⃗=F⃗m=2t î + 3t^2 ĵ Acceleration is defined as ra ...

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Standard IX

Physics

Second Law of Motion

A body of mas...

Question

A body of mass $1$ kg begins to move under the action of a time dependent force $\to F = (2 t^i + 3 t^{2}^j) N,$ where $^i$ and $^j$ are unit vectors along x and y axis. What power will be developed by the force at the time $t$ ?

(2 t^{2} + 3 t^{3}) W

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(2 t^{2} + 4 t^{4}) W

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(2 t^{3} + 3 t^{4}) W

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(2 t^{3} + 3 t^{5}) W

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Solution

The correct option is D $(2 t^{3} + 3 t^{5}) W$
Applying Newton's second law of motion, acceleration, $\to a = \frac{\to F}{m} = 2 t^i + 3 t^{2}^j$

Acceleration is defined as rate of change of velocity,
$\to a = \frac{d \to v}{d t}$
$\to v = \int_{0}^{t} \to a d t$
$\to v = \int_{0}^{t} (2 t^i + 3 t^{2}^j) d t$
$\to v = t^{2}^i + t^{3}^j$

Power, $P = \to F . \to v = (2 t^i + 3 t^{2}^j) . (t^{2}^i + t^{3}^j)$
$P = (2 t^{3} + 3 t^{5}) W$

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A body of mass 1 kg begins to move under the action of a time dependent force →F=(2t^i+3t2^j)N, where ^i and ^j are unit vectors along x and y axis. What power will be developed by the force at the time t?

The correct option is D (2t3+3t5)WApplying Newton's second law of motion, acceleration, →a=→Fm=2t^i+3t2^jAcceleration is defined as rate of change of velocity,→a=d→vdt→v=∫t0→adt→v=∫t0(2t^i+3t2^j)dt→v=t2^i+t3^jPower, P=→F.→v=(2t^i+3t2^j).(t2^i+t3^j)P=(2t3+3t5) W

A body of mass $1$ kg begins to move under the action of a time dependent force $\to F = (2 t^i + 3 t^{2}^j) N,$ where $^i$ and $^j$ are unit vectors along x and y axis. What power will be developed by the force at the time $t$ ?