Question

26. A body of mass 0.2 kg and initially at rest, picks up a velocity of 20 ms' in 10 s.calculate.
(c) distance covered by body :
(d) work done by body :
(e) power developed by body :​

Answer 1

Provided that:

• Mass = 0.2 kg
• Initial velocity = 0 mps
• Final velocity = 20 mps
• Time = 10 seconds

Don't be confused! Initial velocity cames as zero because the body starts from rest as it is initially at rest.

To calculate:

• Distance covered
• Work done
• Power

Solution:

• Distance covered = 100 m
• Work done = 40 J
• Power = 4 Watts

Using concepts:

• Equations of motion:

• First equation of motion to calculate acceleration.

• To calculate distance travelled we can use either second equation of motion or third equation of motion. (Choice may vary.)

• Acceleration formula:

• We can find acceleration by using acceleration formula too! (Choice may vary and yours.)

• Newton's second law of motion that tell us about force formula.

• Work done formula.

• Power formula.

Using formulas:

• Three equations of motion are mentioned below respectively:

$\begin{gathered}\boxed{\begin{array}{c}\\ {\pmb{\sf{Three \: equation \: of \: motion}}} \\ \\ \sf \star \: v \: = u \: + at \\ \\ \sf \star \: s \: = ut + \: \dfrac{1}{2} \: at^2 \\ \\ \sf \star \: v^2 - u^2 \: = 2as\end{array}}\end{gathered}$

• Acceleration formula:

• ${\small{\underline{\boxed{\pmb{\sf{a \: = \dfrac{v-u}{t}}}}}}}$

• Force formula:

• ${\small{\underline{\boxed{\pmb{\sf{Force \: = ma}}}}}}$

• Work done formula:

• ${\small{\underline{\boxed{\pmb{\sf{Work \: done \: = Fs}}}}}}$

• Power formula:

• ${\small{\underline{\boxed{\pmb{\sf{P \: = \dfrac{W}{t}}}}}}}$

Where, a denotes acceleration, u denotes initial velocity, v denotes final velocity, t denotes time taken, m denotes mass, F denotes force, W denotes work done, s denotes displacement or distance or height and P denotes power.

Required solution:

~ Firstly to solve this question there is a need to find out the acceleration so let us find out the acceleration!

By using acceleration formula...

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time} \\ \\ :\implies \sf a \: = \dfrac{dv}{dt} \\ \\ :\implies \sf a \: = \dfrac{\Delta v}{t} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{20-0}{10} \\ \\ :\implies \sf a \: = \dfrac{20}{10} \\ \\ :\implies \sf a \: = 2 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = 2 \: ms^{-2}$

By using first equation of motion...

$:\implies \sf v \: = u \: + at \\ \\ :\implies \sf 20 = 0 + a(10) \\ \\ :\implies \sf 20 = 10a \\ \\ :\implies \sf a \: = \dfrac{20}{10} \\ \\ :\implies \sf a \: = 2 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = 2 \: ms^{-2}$

• Hence, acceleration = 2 m/s²

~ Now let us solve the given parts!

a. Distance covered!?

By using third equation of motion...

$:\implies \sf v^2 - u^2 \: = 2as \\ \\ :\implies \sf (20)^{2} - (0)^{2} = 2(2)(s) \\ \\ :\implies \sf 400 - 0 = 4s \\ \\ :\implies \sf 400 = 4s \\ \\ :\implies \sf s \: = \dfrac{400}{4} \\ \\ :\implies \sf s \: = 100 \: m \\ \\ :\implies \sf Distance \: = 100 \: m$

By using second equation of motion...

$:\implies \sf s \: = ut + \: \dfrac{1}{2} \: at^2 \\ \\ :\implies \sf s \: = 0(10) + \dfrac{1}{2} \times 2(10)^{2} \\ \\ :\implies \sf s \: = 0 + \dfrac{1}{2} \times 2(100) \\ \\ :\implies \sf s \: = 0 + \dfrac{1}{2} \times 200 \\ \\ :\implies \sf s \: = 100 \: m \\ \\ :\implies \sf Distance \: = 100 \: m$

• Henceforth, distance = 100 m

b. Finding work done!?

~ Before that we have to find out the force by using suitable formula!

$:\implies \sf Force \: = Mass \times Acceleration \\ \\ :\implies \sf F \: = ma \\ \\ :\implies \sf F \: = 0.2(2) \\ \\ :\implies \sf F \: = 0.4 \: Newton$

~ Now finding work done by using suitable formula!

$:\implies \sf Work \: done \: = F \times s \\ \\ :\implies \sf Work \: done \: = 0.4 \times 100 \\ \\ :\implies \sf Work \: done \: = 40 \: Joules$

• Hence, work done = 40 J

c. Power developed!?

$:\implies \sf P \: = \dfrac{W}{t} \\ \\ :\implies \sf P \: = \dfrac{40}{10} \\ \\ :\implies \sf P \: = 4 \: Watts \\ \\ :\implies \sf Power \: = 4 \: Watts$

Answer 2

yrr sis

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or unki gf ko btaya kisine?