How Do I Calculate Time with Initial Velocity, Final Velocity, and Distance?

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Discussion Overview

The discussion revolves around calculating the time required to reach a specific final velocity given an initial velocity and a distance traveled. The context includes basic physics concepts related to constant acceleration and average velocity, with a focus on deriving a formula for time based on these parameters.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant seeks a formula to calculate time with given initial velocity, final velocity, and distance, specifically asking for help due to a lack of physics background.
  • Another participant suggests that with constant acceleration, the average speed can be calculated as half the final velocity, leading to a formula for time based on distance and average speed.
  • A further contribution explains that the average velocity is the arithmetic mean of the initial and final velocities, providing a method to derive time from the distance and average velocity.
  • There is a general formula presented for calculating time based on distance and final velocity, emphasizing the relationship between distance, velocity, and time under constant acceleration.

Areas of Agreement / Disagreement

Participants generally agree on the approach to calculating time using average velocity and the relationship between distance and velocity under constant acceleration. However, no explicit consensus on a single formula is established, as different methods are discussed.

Contextual Notes

The discussion does not address potential limitations or assumptions in the formulas presented, such as the conditions required for constant acceleration or the implications of varying initial and final velocities.

Who May Find This Useful

This discussion may be useful for individuals seeking to understand basic kinematic equations, particularly those interested in the relationship between velocity, distance, and time in physics.

Photon713
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Is there a formula that will calculate time when I know the following...?

Initial velocity = 0 Final velocity = 28.14 feet per second and distance traveled = 3 feet.

I would like to know the formula and the time it would take to reach a velocity of
28.14 feet per second if I only have 3 feet to reach that velocity. I would like to
alter the velocity and re-calculate the time.

Thanks for any help...I have no physics or calculus background.
 
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Welcome to PF!

Hi Photon713! Welcome to PF! :smile:

With constant acceleration, the average speed is half the maximum speed:

vaverage = vfinal/2.

Then time = distance/vaverage. :smile:
 
Here's a trick that will help. If an object is moving with a constant acceleration, it "average velocity"- total distance moved, divided by time moved- is equal to the arithmetic average of the beginning and final velocities. In this case, Your average velocity 3/T, where T is the time required and since your final velocity is 28.14 and initial velocity is 0, the average velocity is (28.14+ 0)/2= 14.07 ft/sec. Now you have
3/T= 14.07 ft/sec so T= 3/14.07 seconds.

More generally, to go from velocity 0 to V in distance D, you have an average velocity of D/T= V/2 so T= 2D/V. Of course, that must be done at acceleration V/T.
 
Gentlemen...thank you for your responses. It's exactly what I wanted. Appreciate the welcome and the formula. Regards
 

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