# How Do You Calculate Instantaneous Velocity at a Midpoint in Particle Motion?

• fight_club_alum
In summary,The position of a particle moving along the x axis is given in centimeters by x = 9.35 + 1.03 t3, where t is in seconds.The instantaneous velocity when the particle is midway between its positions at t = 2.00 s and t = 3.00 s is 8.022 cm/s.
fight_club_alum

## Homework Statement

The position of a particle moving along the x axis is given in centimeters by x = 9.35 + 1.03 t3, where t is in seconds. Calculate the instantaneous velocity when the particle is midway between its positions at t = 2.00 s and t = 3.00 s.

## The Attempt at a Solution

f(2)-f(3)/2
then, solve for t, which will be cubic_root(17.5)
add it to the equation (f(to+h)-f(to))/h as h tends to 0

Once you have t, you have to put that value in the equation for v(t). What is that equation and what did you get for the value of t?

fight_club_alum
kuruman said:
Once you have t, you have to put that value in the equation for v(t). What is that equation and what did you get for the value of t?
kuruman said:
Once you have t, you have to put that value in the equation for v(t). What is that equation and what did you get for the value of t?
8.022

kuruman said:
Once you have t, you have to put that value in the equation for v(t). What is that equation and what did you get for the value of t?
I use this equation for the evaluation of tangent, instantaneously, which is in this case is the instantaneous velocity lim h -->0 f(to+h) - f(to) / h

Since you know ##x(t)##, It is better to use $$v(t)=\frac{dx(t)}{dt}.$$

On edit:
fight_club_alum said:
8.022
I disagree with this value. Can you show how you got it?

Last edited:
fight_club_alum
kuruman said:
Since you know ##x(t)##, It is better to use $$v(t)=\frac{dx(t)}{dt}.$$

On edit:

I disagree with this value. Can you show how you got it?
I followed many steps that would be hard to post here

fight_club_alum said:
I followed many steps that would be hard to post here

How can we possibly help if you will not show what you have done? If you know how to take derivatives, it is simple---hardly needing any work. If you don't know how to take derivatives you will need to a bit more work, but it is still manageable.

Just be careful how you write things: when you write f(t0+h) - f(t0), the standard parsing rules for mathematical expressions interprets this as
$$f(t_0+h) - \frac{f(t_0)}{h},$$
which (I hope) you do not intend. If you mean
$$\frac{f(t_0 +h) - f(t_0)}{h}$$
you need to use parentheses, like this: [f(t0+h)-f(t0)]/h. That forces the subtraction in the numerator to occur before the division.

fight_club_alum
What is the value of f(3)? What is the value of f(2)? What is the location half-way between these two locations? What is the time corresponding to this half-way location?

## What is Midway Instantaneous Velocity?

Midway Instantaneous Velocity is a measurement of an object's speed at a specific moment in time. It is the rate of change of an object's position at the midway point between two given time intervals.

## How is Midway Instantaneous Velocity calculated?

To calculate Midway Instantaneous Velocity, the object's position at two different points in time is recorded. Then, the change in position is divided by the time interval between the two points to determine the average velocity. Finally, this average velocity is divided by 2 to calculate the Midway Instantaneous Velocity.

## What is the difference between Midway Instantaneous Velocity and Average Velocity?

The main difference between Midway Instantaneous Velocity and Average Velocity is the time interval used in the calculation. Average Velocity uses the total time interval between two points, while Midway Instantaneous Velocity only considers the change in position at the midway point between the two points in time.

## Why is Midway Instantaneous Velocity important in physics?

Midway Instantaneous Velocity is important in physics because it allows us to study the motion of objects at a specific moment in time. This is useful in understanding acceleration, forces, and other aspects of an object's motion.

## Can Midway Instantaneous Velocity be negative?

Yes, Midway Instantaneous Velocity can be negative. This indicates that the object is moving in the opposite direction of its initial position. It can also signify a change in direction from positive to negative velocity.

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