How Do You Calculate Instantaneous Velocity at Point 2?

[deficiency4math]

Hi,

I was wondering how to solve the instantaneous velocity for this.

I have 3 points which have 5 cm between point 1 and point 2 and 9 cm between point 2 and point 3 (this is easy, i just need to grasp the concept)

The question is "What is the instantaneous velocity for point 2?

How would I figure this out?

thanks

 

[whozum]

Do you have any times?

 

[deficiency4math]

oh, yes, sorry,

the time intervals between the points are 1/40th of a second (lets say)

(sorry, I forgot to post them... I kinda forgot!)

 

[whozum]

Can you give a little background? What kind of motion is going on here, constant acceleration?

 

[deficiency4math]

it would be variable acceleration, because the consecutive distance between 1&2 is 5 and 2&3 9... so let's say that each time, the velocity increases by one.

Would I just take the velocity of 1-2 (5cm per 1/40th of a second) and 2-3 (9cm per 1/40th of a second) and find the average of them to get the instantaneous?

 

[whozum]

it would be variable acceleration, because the consecutive distance between 1&2 is 5 and 2&3 9... so let's say that each time, the velocity increases by one.

Define acceleration in terms of velocity. Does acceleration have to change for velocity to change?

Would I just take the velocity of 1-2 (5cm per 1/40th of a second) and 2-3 (9cm per 1/40th of a second) and find the average of them to get the instantaneous?

I don't know how accurate you need to be, but what I would do is try to figure out the average acceleration. The object is speeding up, so its position function is:

$$x(t) = x_0 + v_0t + 1/2 * at^2$$

We traveled x(t) = 14cm in t=0.05sec. Can you find the acceleration? Can you find the velocity at t=0.025 with this?