# Often asked: When is a particle at rest?

## How do you know when a particle is at rest?

To find when the particle is at rest, we take the velocity (1st derivative formula), set it equal to zero, and solve for t. We find there are two times when this will happen.

## How do you know when a particle is moving to the left?

The particle is considered moving to the left when the velocity function is negative (below the x-axis). The particle is considered not moving at all x-intercepts, and in fact, is changing directions when v(t) changes signs at the x-intercepts.

## What is the position of the particle at time t?

The position of a particle is often thought of as a function of time, and we write x(t) for the position of the particle at time t. The displacement of a particle moving in a straight line is a vector defined as the change in its position.

## How do you find if a particle is speeding up or slowing down?

If 0″>a(t)=p′′(t)>0, the particle is speeding up. If a(t)=p′′(t)<0, the particle is slowing down. If a(t)=p′′(t)=0, then the particle is moving at a constant speed.

## What is the velocity after 3 seconds?

After 3 seconds, the velocity is 4.5+3×1.5=9 m/s.

## How do you tell if a particle is moving in a positive direction?

Example

1. When velocity is negative, the particle is moving to the left or backwards.
2. When velocity is positive, the particle is moving to the right or forwards.
3. When velocity and acceleration have the same sign, the speed is increasing.
4. When velocity and acceleration have opposite signs, the speed is decreasing.
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## At what time is the particle farthest to the left?

Therefore, the particle is farthest left at time t = 3 when its position is x(3) = -10. By the Intermediate Value Theorem, there are three values of t for which the particle is at x(t) = -8. this interval v < 0 and v is increasing. answer.

## Will the particle move to the right or to the left?

When the velocity, or the derivative of your function, is negative, it is moving left. When the velocity (derivative) is positive, it is moving to the right. When the velocity is equal to zero, it is stopped.

## Is the particle speeding up or slowing down at t 1?

So it is slowing down, according to your definition, between [0,1] and [2,3], and speeding up otherwise. A particle usually speeds up when the velocity and the acceleration have the same signs. It slows down when the acceleration and velocity signs are different.

## Can velocity be negative?

Velocity is a vector quantity. If we’re moving along a line, positive velocity means we’re moving in one direction, and negative velocity means we’re moving in the other direction. Speed is the magnitude of the velocity vector, and hence is always positive.

## Is position a distance or displacement?

Position is the location of the object (whether it’s a person, a ball, or a particle) at a given moment in time. Displacement is the difference in the object’s position from one time to another. Distance is the total amount the object has traveled in a certain period of time.

## Is the particle ever at rest?

Common sense says a particle is at rest when its velocity is 0 (i.e., not moving). So let’s set v(t) = 0. Solving for t, we get t = 3 and t = 1 seconds. The particle is at rest after 1 seconds and 3 seconds.

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## What is the particle’s position at t 3.0 s?

Its initial position is zo = 1.0 m at to 0 s.