Question

A force is applied on a body of mass 25 kg moving with a velocity of 3 m/s. the body attains a velocity of 50 m/s in 2 seconds. Calculate the work done by the body and Power developed.​

Answer 1

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Answer 2

Answer:

A force is acting on a body of mass 25 kg moving with a velocity of 3 m/s. the body attains a velocity of 50 m/s in 2 seconds, the work done by the body is $31137.5Nm$ and Power developed is $15568.7Nm/s$

Explanation:

• The work done (W) is the product of the force (F) applied and displacement(d) of the body due to the applied force, that is

        $W=F.d$

• From Newton's second law $F=ma$

• The acceleration is the change in velocity with time $a=(v-u)/t$

• From the equation of motion, the distance moved by an accelerated body is      $s=ut+\frac{1}{2}at^{2}$

• Power of a body is the work done per unit done $P=W/t$

From the question, we have

mass of the body $m=25kg$

the initial velocity of the body $u=3m/s$

the final velocity $v=50m/s$

time taken for this change $t=2s$

⇒ the acceleration of the body

$a=\frac{50-3}{2} =47/2=23.5m/s^{2}$

now force on the body $F=25*23.5=587.5N$

the distance traveled $s=3*2+\frac{1}{2} *23.5*2^{2} =53m$

therefore required work done $W=587.5*53=31137.5Nm$

power of the body $P=31137.5/2=15568.7Nm/s$