Q. 64

Expert-verified
Found in: Page 157

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# At , an object of mass is at rest at on a horizontal, frictionless surface. Starting at , a horizontal forcé is exerted on the object.a. Find and graph an expression for the object's velocity at an arbitrary later time .b. What is the object's velocity after a very long time has elapsed?

Part(a): The expression of particle velocity at any time is .

Part (b): Objects velocity after a very long time is .

See the step by step solution

## Part (a) Step 1: Given.

Force on the particle, .

Velocity at time .

Position at time .

## Part (b): Step 2: Formula used.

Force on a object is given by the equation:

Here,

is the mass.

is the acceleration.

## Part (b): Step 3: Calculation

Force on the particle is given as:

Force on an object is given by the equation

On comparing Eq. and Eq.{}

The velocity of a particle at a time is obtain by integrating the above equation,

## Part (b) Step 4: Calculation.

Here,

is the arbitrary constant of integration

Apply the boundary condition that at time the velocity of the particle is .

Plugging the values in the above equation

Substitute the value of in Eq. (

## Part (b) Step 5: GIven.

The expression of particle velocity at any time is .

## Part (b): Step 6; Calculation.

Expression of particle velocity at any time is:

The velocity of a particle is an exponent function of time, therefore as the time elapsed the magnitude of exponent term will be .

And the velocity of the particle is given as:

## Step 7: Conclusions.

Part (a): Expression of particle velocity at any time is .

Part (b): Objects velocity after a very long time is .