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Q. 64

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

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

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 .

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