Question

A body of mass 2 kg is accelerated from rest to a velocity. 20 ms$^{–1}$ in 5 s. What is the work done and power consumed.​

Answer 1

Explanation:

Given:-

• Mass of the body (m) = 2kg

• Initial velocity (u) = 0m/s [ Body starts from rest ]

• Final velocity (v) = 20m/s

• Time taken (t) = 5 sec

To Find:-

• The work done by the body.

• Power consumed by the body.

Solution:-

Using 1st equation of motion:-

$\sf \implies v = u + at$

$\sf \implies 20 = 0 + a(5)$

$\sf \implies 5a = 20$

$\sf \implies a = \dfrac{20}{5}$

$\sf \implies a = 4m/s^2$

$\therefore \underline{\sf \: Acceleration = 4m/s^2 \: }$

Now, let us find distance by

Using 3rd equation of motion:-

$\sf \implies S = ut + \dfrac{1}{2}at^2$

$\sf \implies S = 0(5) + \dfrac{1}{2} \times 4 \times 5 \times 5$

$\sf \implies S =\dfrac{100}{2}$

$\sf \implies S = 50m$

$\therefore \underline{\sf \: Distance = 50m\: }$

$\sf Force = Mass \times Acceleration$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 4$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: = 8N$

$\sf Work \: done = Force \times Displacement$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 8 \times 50$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 400J$

$\dashrightarrow \underline{\boxed{\therefore \sf Work \: done = 400J}}$

$\sf Power = \dfrac{Work \: done}{Time}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \dfrac{400}{5}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 80W$

$\dashrightarrow \underline{\boxed{\sf \therefore Power \: consumed= 80W}}$

Answer 2

$\large{\textbf{\underline{Given:-}}}$

✒Mass = 2kg

✒Final Velocity = 20m/s

✒Initial Velocity = 0m/s [as object starts from rest]

✒Time = 5sec

$\large{\textbf{\underline{Find:-}}}$

✑Work Done

✑Power Consumed

$\large{\textbf{\underline{Solution:-}}}$

☯$\underline{\textsf{we know work done:-}}$

$\huge{\underline{\boxed{\sf Change \: in \: Kinetic \: Energy}}}$

$\implies\sf \dfrac{1}{2} m \big\lgroup{v}^{2} - {u}^{2}\big\rgroup$

$\gray{\sf where} \footnotesize{\begin{cases} \pink{\sf m = 2kg} \\ \green{\sf v =20m/s} \\ \purple{\sf u = 0m/s} \end{cases}}$

☯$\underline{\textsf{Substituting these values in the formula:-}}$

$\dashrightarrow\sf \dfrac{1}{2} m \big\lgroup{v}^{2} - {u}^{2}\big\rgroup$

$\dashrightarrow\sf \dfrac{1}{2} \times 2 \times \big\lgroup{20}^{2} - {0}^{2}\big\rgroup$

$\dashrightarrow\sf \dfrac{2}{2}\times \big\lgroup400 - 0\big\rgroup$

$\dashrightarrow\sf 400 J$

$\small{\therefore \underline{\textsf{Work Done = 400J}}}$

☯$\underline{\textsf{Now, using:-}}$

$\implies\sf Power = \dfrac{Work\:Done}{Time}$

$\pink{\sf where} \footnotesize{\begin{cases} \purple{\sf Work \: Done = 400J} \\ \blue{\sf Time = 5s} \end{cases}}$

✯$\underline{\textsf{Substituting these values in the formula:-}}$

$\dashrightarrow\sf Power = \dfrac{Work\:Done}{Time}$

$\dashrightarrow\sf Power = \dfrac{400}{5}$

$\dashrightarrow\sf Power = 80W$

$\small{\therefore \underline{\textsf{Power = 80W}}}$