Question

Power delivered to a paticle varies with time as P = (3t^(2) - 2t) watt, where 't' is in seconds, then change in its kinetic energy between time t = 1 to t = 3s.

Answer 1

Answer:

18

Explanation:

as we know that power =work done per unit time OR energy per unit time

• so P=3t^2-2t
• energy =power ×time =integration of power with respect to time
• We get energy={t^3-t^2} and also applying limit
• we get 27-9-1+1=18

Answer 2

Answer:

Given:

Power delivered to a particle is a function of time as follows ;

$P = 3 {t}^{2} - 2t$

To find:

Change in Kinetic energy between t = 1 to t = 3 sec.

Concept:

According to Work - Energy Theorem , ww can say that the total work work done by all the forces acting on the system is equal to the change in Kinetic Energy.

Also Power is the rate of Work done .

Calculation:

$work = \int \: P \: dt$

$= > work = \int \: ( 3{t}^{2} - 2t) \: dt$

Putting the limits :

$= > work = \displaystyle \: \int_{1}^{3} \: ( 3{t}^{2} - 2t) \: dt$

$= > work = \bigg \{ {t}^{3} \bigg \}_{1}^{3} \: - \bigg \{ {t}^{2} \bigg \}_{1}^{3}$

$= > work = 26 - 8 = 18 \: joule$

So change in Kinetic energy is same as the work done.

So final answer :

$\boxed{ \red{ \huge{ \bold{ \sf{\Delta KE \: = 18 \: joule}}}}}$