Question

calculate the power exerted in pulling a cart appling a froceof 125N at a constant speed of 15m/s​

Answer 1

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: Given :- }}}$

$\to\textsf{ A force of 125 N is applied.}\\\to\textsf{ Force is applied at a speed of 15m/s.}$

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: To \ Find :- }}}$

$\to\textsf{ The Power exrerted in pulling the cart .}$

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: Answer :- }}}$

We know that Power is defined as the rate of doing work , that is $\sf P =\dfrac{Work}{Time}$ .Also we know that Work is the dot product of Force and Displacement , that is $\sf Work = F.s$ So we have ,

$\sf:\implies \pink{Power = \dfrac{Work}{Time}}\\\\\sf:\implies Power = \dfrac{Force \times displacement}{Time}\\\\\sf:\implies P =\dfrac{ F \times s }{t}\\\\\sf:\implies P = F \times \dfrac{s}{t}\\\\\sf:\implies P = F \times v \qquad\qquad \bigg\lgroup \red{\bf Speed = \dfrac{Distance}{Time}}\bigg\rgroup \\\\\sf:\implies P = 125 N \times 15m/s \\\\\sf:\implies\boxed{\pink{\frak{ Power = 1875 Watts }}}$

$\underline{\blue{\sf \therefore Hence \ the \ Power \ exrerted \ is \textsf{\textbf{1875 Watts }}. }}$

Answer 2

We know,

P = W/t, but W = F s

⇒ P = (Fs)/t, again s/t = v.

So, P = Fv

Now as per condition, F = 125 N

Speed = 15 m/s

So, P = Fv = (125 N)(15 m/s)

⇒ P = 1875 W or 1.875 kW.

∴ The power exerted in pulling a cart by applying force of 125 N at a constant speed of 15 m/s is 1.875 kW.