Question

Power delivered to a particle varies with the time as P=(2t+3)w , where t is time in second . The change in kinetic energy between t=0s to t=2s will be

Answer 1

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

$\large{\star \: P = 2t +3}$

Kinetic energy = ?.

$\huge{\bold{\underline{Explanation:-}}}$

As we know,

$\large{\bold{ P = \frac{dw}{dt}}}$

Now,

$\large{dw = P .dt}$

Taking over a large time interval.

$\large{ \displaystyle\int dw = \displaystyle\int P.dt}$

Applying limits,

$\large{ \displaystyle\int^w_0 dw = \displaystyle\int^2_0 P.dt}$

Substituting the power value.

$\large{ \displaystyle\int^w_0 dw = \displaystyle\int^2_0 (2t + 3).dt}$

Now,

Integrating,

$\large{ W = \left[ \dfrac{2t^2}{2} + 3t \right]^2_0}$

$\large{ W = \left[ \dfrac{ \cancel{2}t^2}{ \cancel{2}} + 3t \right]^2_0}$

Now,

$\large{W = \left[t^2 + 3t \right]^2_0}$

Substituting the value of time,

$\large{W = (2)^2 + 3(2)}$

$\large{W = 4 + 6}$

$\large{\boxed{W = 10 \: J}}$

As we know, the Kinetic energy is equal to work done.

$\large{ \therefore K.E = W}$

$\huge{\boxed{\boxed{K.E = 10 \: J}}}$

So, the change in Kinetic energy is 10 Joules.

Answer 2

The kinetic energy of an object is 10 J.

Explanation:

Power delivered to a particle varies with the time as :

$P=(2t+3)\ W$

We know that the rate at which work is done is called power. It is given by :

$P=\dfrac{dW}{dt}$

W = work done

$W=\int\limits {P.dt}$

$W=\int\limits^2_0 {(2t+3)\ dt}$

$W=\dfrac{2t^2}{2}+3t|_0^2$

$W=\dfrac{2(2)^2}{2}+3(2)$

W = 10 J

We know that the work done is equal to the kinetic energy of an object. So, the kinetic energy of an object is 10 J.

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Topic : Kinematics

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