# At what time is the particle at rest?

## At what time is the particle 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.

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

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.

What is the body’s acceleration each time the velocity is zero?

Find the body’s speed each time the acceleration is zero. Since a(t)=6t-12 = 0 when t = 2 and the speed function is sp(t) = |v(t)|, the answer is |v(2)| = 3m/sec.

At what time intervals is the particle speeding up?

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 a particle with zero acceleration speed up?

yes particles with zero acceleration can speed up by the chande of direction in particles.

### Is acceleration a change in speed or direction?

Acceleration is the rate of change of velocity. Usually, acceleration means the speed is changing, but not always. When an object moves in a circular path at a constant speed, it is still accelerating, because the direction of its velocity is changing.

Is the particle speeding up or slowing down at T 3?

So think of it as the particle is slowing down in the left direction and therefore you are not speeding up, you are actually slowing down. It is only when the particle switches direction to the right that it is speeding up (i.e. velocity turns positive at t > 3).

How do you know if speed is increasing or decreasing calculus?

Speed is increasing when the velocity and acceleration have the same sign. Speed is decreasing when the velocity and acceleration have different signs.

## How do you tell if an object is speeding up or slowing down on a graph?

That is, if the line is getting further away from the x-axis (the 0-velocity point), then the object is speeding up. And conversely, if the line is approaching the x-axis, then the object is slowing down.

### Is the particle in Figure 1 speeding up slowing down or can you tell?

Without numbers on the dots we cannot tell if the particle in the figure is moving left or right, so we can’t tell if it is speeding up or slowing down. If the particle is moving to the right it is speeding up. If it is moving to the left it is slowing down.

What does constant velocity look like on a graph?

The principle is that the slope of the line on a position-time graph reveals useful information about the velocity of the object. If the velocity is constant, then the slope is constant (i.e., a straight line). If the velocity is changing, then the slope is changing (i.e., a curved line).

What does the slope of a velocity time graph indicate?

The slope of a velocity graph represents the acceleration of the object. So, the value of the slope at a particular time represents the acceleration of the object at that instant.

## What happens to velocity when acceleration is constant?

Sometimes an accelerating object will change its velocity by the same amount each second. This is referred to as a constant acceleration since the velocity is changing by a constant amount each second. An object with a constant acceleration should not be confused with an object with a constant velocity.

### Why is acceleration negative when velocity is positive?

This object below moves in the positive direction with a changing velocity. An object which moves in the positive direction has a positive velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion (in this case, a negative acceleration).

Is there a negative velocity?

Negative velocity just means velocity in the opposite direction than what would be positive. From the math point of view, you cannot have “negative velocity” in itself, only “negative velocity in a given direction”. The velocity is a 3-dimension vector, there is no such thing as a positive or negative 3D vector.

Can a final velocity be negative?

Since the final position of the object (rfinal) may be either positive, negative, or zero, and either larger, smaller, or the same as the initial position (rinitial), the velocity may be positive, negative, or zero. The sign of the velocity depends on the coordinate system chosen to define the position.

## Is negative velocity going backwards?

An object moving in the negative direction (negative velocity) is speeding up. A positive velocity means it’s going in the positive direction (like forwards), and a negative direction is backwards.

### What does negative velocity indicate?

Velocity comes with direction, it indicates a speed at a direction. If velocity becomes negative, it is that speed in the opposite direction.

Can we have constant speed but not constant velocity?

If a car moves with a constant speed, can you say that it also moves with a constant velocity? Give an example to support your answer. No, you could be going around a corner at constant speed. Your velocity is then not constant.

What is an example of negative velocity?

A negative velocity means that the object which has the negative velocity is moving in the opposite direction of an object moving at a positive velocity. If the object is speeding up then its acceleration vector is directed in the same direction as its motion (in this case, a negative acceleration).

## What happens to velocity when acceleration is negative?

If velocity and acceleration have the same sign, you speed up. If velocity and acceleration have opposite signs, you slow down. Negative velocity = You move backwards. Negative acceleration = You slow down or you go faster in the backwards direction.

### Does a positive acceleration always mean an increase in speed?

If the speed is increasing, the car has positive acceleration. When the car slows down, the speed decreases. The decreasing speed is called negative acceleration. In both cases, the car is accelerating, but one acceleration is positive and one is negative.