# When is a particle speeding up or slowing down?

• Alain12345
In summary, the conversation discusses determining the velocity and acceleration functions for a particle moving on a vertical line, as well as when the particle is moving up, down, speeding up, and slowing down. The interval chart method is suggested for determining these intervals, and it is noted that the particle is speeding up whenever the acceleration and velocity have the same sign.
Alain12345
I need help with a question asking if the particle is speeding up or slowing down.

A particle moves on a vericle line. It's position, s, in metres at t seconds is given by s(t)= t^3-9t^2+24t

a) determine the velocity and acceleration functions
I got v(t)= 3t^2-18t+24 and a(t)= 6t-18

b) When is the particle moving up? Down?
I got when 0<t<2, t>4 and it's slowing down at 2<t<4

c) When is the particle speeding up? Slowing down?

I thought that I have to use a similar method to part b and make an interval chart, but I don't think I'm doing it right. I used the a(t) function and found the zero and used that in the chart.

Can someone help me out? Thanks.

It's speeding up whenever the acceleration and velocity are either both negative, or both positive. This is because then the acceleration and velocity are both in the same direction. When the acceleration is negative, and velocity positive, or vice versa, the particle is slowing down.

Also, in part b, you write it's slowing down for 2<t<4, when it should say "moving down". You might want to make sure you didn't write that down on your answer sheet too :p

## 1. What is the definition of acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is measured in meters per second squared (m/s^2).

## 2. How do you determine if a particle is speeding up or slowing down?

If a particle's velocity is increasing, it is considered to be speeding up. If its velocity is decreasing, it is considered to be slowing down. This is determined by looking at the sign of the particle's acceleration. A positive acceleration indicates speeding up, while a negative acceleration indicates slowing down.

## 3. What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of how fast an object is moving in a specific direction. Velocity takes into account both speed and direction, while speed only looks at how fast an object is moving.

## 4. Can a particle's velocity change without changing its speed?

Yes, a particle's velocity can change without changing its speed. This can happen if the particle changes direction while moving at a constant speed. For example, if a car is traveling at a constant speed but turns a corner, its velocity will change even though its speed remains the same.

## 5. How does acceleration affect the motion of a particle?

Acceleration affects the motion of a particle by changing its velocity. If a particle is accelerating, its velocity will change by either increasing or decreasing. This change in velocity will in turn affect the particle's speed and its overall motion.

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