## 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**

**When**velocity is negative, the**particle is moving**to the left or backwards.**When**velocity is**positive**, the**particle is moving**to the right or forwards.**When**velocity and acceleration have the same sign, the speed is increasing.**When**velocity and acceleration have opposite**signs**, the speed is decreasing.

## 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.

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

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