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# 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) = et + tet. What is the average velocity of the particle from time 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(0.9t). 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!

## 1 Comment

1. Watson Hal says:

So many helpful examples, thank you!