Question

A particle of mass $M$, starting from rest, undergoes uniform acceleration. If the speed acquired in time $T$ is $V$, the power delivered to the particle is

• A. $\frac{MV^2}{T}$
• B. $\frac{1}{2}\frac{MV^2}{T^2}$
• C. $\frac{MV^2}{T^2}$
• D. \(\frac{1}{2}\frac{MV^2}{T}\)

Answer 1

The Correct Option is D

To solve the problem of determining the power delivered to a particle of mass $M$ starting from rest and undergoing uniform acceleration to achieve a speed $V$ in time $T$, we can use the following physics principles and equations.

Step 1: Understand the concept of power in physics.

Power is defined as the rate at which work is done. If a force $F$ acts on a particle causing displacement $s$, the work done is $W = F \cdot s$. The average power, therefore, is given by:

Power = \frac{Work}{Time} = \frac{W}{T}

In terms of kinetic energy, since the particle is initially at rest and achieves speed $V$, the work done on the particle is equal to its change in kinetic energy which can be expressed as:

Work = \frac{1}{2} M V^2

Step 2: Calculate the power delivered.

The power delivered to the particle is the change in kinetic energy per unit time:

Power = \frac{\Delta K.E.}{T} = \frac{\frac{1}{2} M V^2}{T}

This gives us the formula for power:

Power = \frac{1}{2} \frac{M V^2}{T}

Conclusion: The correct option for the power delivered to the particle is \(\frac{1}{2}\frac{MV^2}{T}\).