Constant acceleration and time

In summary, the formula for calculating time with given initial velocity, final velocity, and distance traveled is T = 2D/V, where D is the distance traveled and V is the average velocity (half of the final velocity). This formula can be used to calculate the time it would take to reach a given velocity with only a certain distance to travel.
  • #1
Photon713
19
0
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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  • #2
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:
 
  • #3
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.
 
  • #4
Gentlemen...thank you for your responses. It's exactly what I wanted. Appreciate the welcome and the formula. Regards
 

1. What is constant acceleration?

Constant acceleration is the rate at which an object's velocity changes over time remains constant. This means that the object's speed increases or decreases by the same amount every second.

2. How is constant acceleration calculated?

Constant acceleration can be calculated by dividing the change in velocity by the change in time. This is represented by the formula a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. What is the difference between constant acceleration and uniform acceleration?

Constant acceleration and uniform acceleration are often used interchangeably, but they have a slight difference. Constant acceleration means that the acceleration remains the same throughout the entire motion, while uniform acceleration means that the acceleration is constant but not necessarily the same as the acceleration at any given point.

4. How does time affect an object's acceleration?

Time plays a crucial role in determining an object's acceleration. The longer the time, the more an object's velocity changes, leading to a greater acceleration. This is why it is essential to measure time accurately in experiments involving constant acceleration.

5. Can an object have constant acceleration and changing velocity?

Yes, an object can have constant acceleration and changing velocity. This is because acceleration is a measure of how velocity changes over time, and the velocity can change even if the acceleration remains constant. For example, if an object is thrown upwards, it will have a constant acceleration due to gravity, but its velocity will change as it moves against the force of gravity.

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