# The average velocity of the point - numerical value of t

• Poetria
In summary, the conversation discusses finding the numerical value of t in an equation for the average velocity of a point in motion during the first t seconds. The solution involves finding the initial position at t=0 and determining the displacement at t=3/2. The conversation also mentions the importance of not assuming t=0 due to the possibility of dividing by 0.

## Homework Statement

During the first t seconds of motion, the average velocity of the point is zero. What is the numerical value of t?

## The Attempt at a Solution

I don't understand this question. I understand that the average velocity is zero if the displacement in the denominator is zero. E.g. if a body is moving in a circle. Or if a body moves to the right and then to the left and distances cancel out. But how could you give the numerical value of t?
I thought t tended to zero (as a limit): 0.0000000001 but it is wrong.
Am I overlooking something obvious?

I think we're missing some context here. Is this part of a larger question? (The problem mentions "the point", not "a point", so it seems to be referring to something previously defined).

Poetria
Oh yes, silly me. This is an equation from the previous question. I will do it now. That's English for you. Many thanks.

x(t)=2t^2−3t−4

So at time t=0, what's the initial position according to your equation?

When is the position again that value?

Poetria
It is simple now.
I need the displacement = 0 so

at t = 0 initial position x(i) is -4.

The displacement:
(2t^2−3t−4)-(-4)=0
2t^2−3t=0
t=3/2

I can't assume that t=0 because you can't divide by 0. (the average velocity = displacement/time elapsed)

2*(9/4)-3*(3/2)=9/2-9/2=0 :)

Many thanks. :) :) :)

## 1. What is the definition of average velocity?

The average velocity is the change in position of an object divided by the change in time. It is a measure of how fast and in what direction an object is moving over a certain period of time.

## 2. How do you calculate the average velocity of a point?

The average velocity of a point is calculated by taking the difference between the final position and initial position of the point and dividing it by the time elapsed between the two positions.

## 3. What is the unit of measurement for average velocity?

The unit of measurement for average velocity is distance per time, such as meters per second or feet per hour.

## 4. Can the average velocity of a point be negative?

Yes, the average velocity of a point can be negative. This indicates that the object is moving in the opposite direction of the chosen coordinate system.

## 5. How is average velocity different from instantaneous velocity?

Average velocity is calculated over a certain period of time, while instantaneous velocity is the velocity of an object at a specific moment in time. Average velocity takes into account the overall motion of an object, while instantaneous velocity focuses on the object's exact velocity at a given point.