# Thread: Particle movement through space.

1. ## Particle movement through space.

A particle moves according to a law of motion s = f(t), t >= 0, where t is measured in seconds and s in feet.

Find the velocity at time t.
What is the velocity after 3 s?
When is the particle at rest?
When is the particle moving in the positive direction?
Find the total distance traveled during the first 8 seconds.
Find the acceleration at time t after 3 s.
When is the particle speeding up? When is it slowing down?

The equation is f(t) = .01t^4 -.04t^2

I don't quite understand how do to this problem so a complete explanation would be best.

2. Originally Posted by Neversh
A particle moves according to a law of motion s = f(t), t >= 0, where t is measured in seconds and s in feet.

Find the velocity at time t.
What is the velocity after 3 s?
When is the particle at rest?
When is the particle moving in the positive direction?
Find the total distance traveled during the first 8 seconds.
Find the acceleration at time t after 3 s.
When is the particle speeding up? When is it slowing down?

The equation is f(t) = .01t^4 -.04t^2

I don't quite understand how do to this problem so a complete explanation would be best.
Velocity is the derivative of the position function.
The derivative of $\displaystyle t^n$ is $\displaystyle nt^{n-1}$

It will be at rest when the velocity is 0.
It will be moving "in the positive direction" when the velocity is positive.
The "total distance traveled" is the integral of the absolute value of the velocity function.

The acceleration is the derivative of the velocity function.
It will be speeding up when the acceleration is positive.
It will be slowing down when the acceleration is negative.

Now try it.

3. Originally Posted by Neversh
A particle moves according to a law of motion s = f(t), t >= 0, where t is measured in seconds and s in feet.

Find the velocity at time t.
What is the velocity after 3 s?
When is the particle at rest?
When is the particle moving in the positive direction?
Find the total distance traveled during the first 8 seconds.
Find the acceleration at time t after 3 s.
When is the particle speeding up? When is it slowing down?

The equation is f(t) = .01t^4 -.04t^2

I don't quite understand how do to this problem so a complete explanation would be best.
You have asked several of these questions now - all the same except for the function. Please refer to the other replies in the other threads.