Q. 64

Expert-verifiedFound in: Page 157

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 .

Force on the particle, .

Velocity at time .

Position at time .

Force on a object is given by the equation:

Here,

is the mass.

is the acceleration.

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,

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. (

The expression of particle velocity at any time is .

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:

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

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

94% of StudySmarter users get better grades.

Sign up for free