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# Category Archives: Particle Motion

## Particle Motion calculus problems

## Average Velocity of a Particle example question

The velocity, in feet per second, of a particle moving along the ** x**-axis is given by the function

**(**

*v**t*) =

*e*+

^{t}*te*. What is the average velocity of the particle from time

^{t}*t*= 0 to time

*t*= 3?

Solution to this **Particle Motion** calculus practice problem is given in the video below!

## Number of Times Velocity of a Particle is Zero example problem

The position of an object attached to a spring is given by , where *t* is time in seconds. In the first 4 seconds, how many times is the velocity of the object equal to 0?

Solution to this **Particle Motion** calculus practice problem is given in the video below!

## Times When a Particle is at Rest example

A particle moves along the * x*-axis so that at time

*t*≥ 0 its position is given by . At what time

*t*is the particle at rest?

Solution to this **Particle Motion** calculus practice problem is given in the video below!

## Height of a Particle at its Maximum Upward Velocity example question

The height *h*, in meters, of an object at time *t* is given by . What is the height of the object at the instant when it reaches its maximum upward velocity?

Solution to this **Particle Motion** calculus practice problem is given in the video below!

## Acceleration of a Particle at Time *t* example problem

A particle moves along the ** x**-axis so that at any time

*t*≥ 0, its velocity is given by

*v*(

*t*) = 3 + 4.1cos(0.9

*t*). What is the acceleration of the particle at time

*t*= 4?

Solution to this **Particle Motion** calculus practice problem is given in the video below!

## HARD Velocity Acceleration of a Particle example

At time *t* ≥ 0, the acceleration of a particle moving on the x-axis is *a*(*t*) = *t* + sin(*t*). At *t* = 0, the velocity of the particle is -2. For what value of *t* will the velocity of the particle be zero?

Solution to this **Particle Motion** calculus practice problem is given in the video below!

## Maximum Acceleration of a Particle example question

Find the maximum acceleration attained on the interval 0 ≤ *t* ≤ 3 by the particle whose velocity is given by

Solution to this **Particle Motion** calculus practice problem is given in the video below!

## Position of a Particle at Time t When its Velocity is First Equal To Zero example problem

A particle moves along the ** x**-axis so that at any time

*t*≥ 0, its velocity is given by . The position of the particle is 3 at time

*t*= 0. What is the position of the particle when its velocity is first equal to 0?

Solution to this **Particle Motion** calculus practice problem is given in the video below!

## Specific Velocity of a Particle using its Acceleration example

A particle moves along the ** x**-axis so that at any time

*t*> 0, its acceleration is given by . If the velocity of the particle is 2 at time

*t*= 1, find the velocity of the particle at time

*t*= 2.

Solution to this **Particle Motion** calculus practice problem is given in the video below!

## Time When the Particle is FARTHEST to the Right example question

A particle moves along the ** x**-axis so that its acceleration at any time

*t*is . If the initial velocity of the particle is 6, at what time

*t*during the interval 0 ≤

*t*≤ 4 is the particle farthest to the right?

Solution to this **Particle Motion** calculus practice problem is given in the video below!

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