Question

A body of mass $m$ accelerates uniformly from rest to $v_{1}$ in time $t_{1} .$ The instantaneous power delivered to the body as a function of time $t$ is [2004] (A) $\frac{m v_{1} t^{2}}{t_{1}}$ (B) $\frac{m v_{1}^{2} t}{t_{1}^{2}}$ (C) $\frac{m v_{1} t}{t_{1}}$ (D) $\frac{m v_{1}^{2} t}{t_{1}}$

Name: Problem 120, Chapter 4: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-06T14:55:51-08:00
Duration: 2 min 13 s
Channel: Dheeraj Sharma
Description: A body of mass m accelerates uniformly from rest to v1 in time t1 . The instantaneous power delivered to the body as a function of time t is [2004] (A) (m v1 t^2)/(t1) (B) (m v1^2 t)/(t1^2) (C) (m v1 t)/(t1) (D) (m v1^2 t)/(t1)

   A body of mass $m$ accelerates uniformly from rest to $v_{1}$ in time $t_{1} .$ The instantaneous power delivered to the body as a function of time $t$ is [2004]
(A) $\frac{m v_{1} t^{2}}{t_{1}}$
(B) $\frac{m v_{1}^{2} t}{t_{1}^{2}}$
(C) $\frac{m v_{1} t}{t_{1}}$
(D) $\frac{m v_{1}^{2} t}{t_{1}}$

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 4, Problem 120

Instant Answer

Solved by Expert Dheeraj Sharma

10/06/2021

Step 1

We can use the equation of motion to find the acceleration of the body. The equation of motion is given by: \[v = u + at\] where $v$ is the final velocity, $u$ is the initial velocity, $a$ is the acceleration, and $t$ is the time. Here, $v = v_{1}$, $u = 0$ (since Show more…

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A body of mass $m$ accelerates uniformly from rest to $v_{1}$ in time $t_{1} .$ The instantaneous power delivered to the body as a function of time $t$ is [2004] (A) $\frac{m v_{1} t^{2}}{t_{1}}$ (B) $\frac{m v_{1}^{2} t}{t_{1}^{2}}$ (C) $\frac{m v_{1} t}{t_{1}}$ (D) $\frac{m v_{1}^{2} t}{t_{1}}$

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Key Concepts

Uniform Acceleration

In uniformly accelerated motion, the acceleration remains constant over time, which leads to a linear relationship between velocity and time. This concept is essential for determining how velocity evolves from the initial value (often zero) to a final value after a specific time interval.

Newton's Second Law

Newton's Second Law, formulated as F = ma, establishes a direct connection between the net force acting on an object, its mass, and its acceleration. This relationship is crucial for linking the constant force applied during uniform acceleration to the mass of the object.

Instantaneous Power

Instantaneous power is defined as the rate at which work is done at a specific moment in time. It is calculated as the product of the instantaneous force and the instantaneous velocity (P = F × v), making it an important concept when analyzing energy transfer during non-uniform processes over time.

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