Constant velocity formula help

In summary: Vf^2=Vi^2+2ad. The final velocity would be Vf2= 92= 81 m/s. So, the formula is very helpful in calculating the final velocity if you know the starting and ending velocity but not the distance.
  • #1
COCoNuT
35
0
can someone tell me what these formulas do?

constant velocity(when velocity is constant, which is 0 right?, you use these formulas)...

1.) a(t) = 0 <== when constant velocity, a(t) = 0 right?
2.) v(t) = Vi(what is v(t)? vi = initial)
3.) x(t) = Xi + ViT (what is this formula used for? what is x(t)?i know that Vi= initial velocity, T= time) is x(0) equal to distance and height.

constant acceleration:
4.) a(t) = a(0) (<--- what does this mean?)
5.) v(t)= Vi + at (<--- what is v(t), and is this used to find the final velocity?)
6.) x(t) = Xi + ViT + 1/2at^2 (<--- what is this formula used for? what is it trying to find? what is x(t)? is x(0) equal to distance and height?)

and this formula, which i don't know what it's used for at all, but i know it's important:
Vf^2 = Vi^2 +2ad (d= distance traveled)

sorry for all the questions, but i think if i understand these formulas more, i would be able to do my physics homework easier, because i ALWAYS have trouble trying to find which formula to use.
 
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  • #2
COCoNuT said:
can someone tell me what these formulas do?

constant velocity(when velocity is constant, which is 0 right?, you use these formulas)...

"1.) a(t) = 0 <== when constant velocity, a(t) = 0 right?"
Assuming that "a(t)" is an acceleration function (you didn't tell us that!), accleration is defined as rate of change of velocity so, yes, it velocity doesn't change, the acceleration is 0: a(t)= 0.

"2.) v(t) = Vi(what is v(t)? vi = initial)"
Are you still assuming that velocity is a constant? If that is true, then yes, velocity at all times, v(t), is that constant and, in particular is the same as the initial velocity: v(t)= vi, a constant function.

"3.) x(t) = Xi + ViT (what is this formula used for? what is x(t)?iknow that Vi= initial velocity, T= time) is x(0) equal to distance and height."
If your constant velocity is vi then the distance moved in time T is vi times T. If your intitial distance from some 0 point was xi then your new distance will be xi plus the distance moved: x(t)= xi+ viT.

"constant acceleration:
4.) a(t) = a(0) (<--- what does this mean?)"
Is it the word "constant" you are having trouble with? a(t) is the acceleration at time t. a(0) is the acceration when t= 0. Since the acceleration is constant, it doesn't change- no matter what t is, the acceleration is still the same as it was at t= 0: a(t)= a(0).

"5.) v(t)= Vi + at (<--- what is v(t), and is this used to find the final velocity?)"
v(t) is the velocity at time t. Yes, it can be used to find the final velocity- it can be used to find the velocity at any time. Acceleration is defined as the rate of change of velocity. It is defined by a= (change in v)/t so, multiplying on both sides by t, change in v= at. Add that change to the initial velocity: v(t)= vi+ change in v= vi+ at.

"6.) x(t) = Xi + ViT + 1/2at^2 (<--- what is this formula used for? what is it trying to find? what is x(t)? is x(0) equal to distance and height?)"
x(t) is position of an object (which might be "height" if the motion is vertical) at time t. x(0) is the position of the object when t= 0. It is the distance from whatever point was chosen as the "reference". It can be height if you are measuring vertically. As long as the acceleration is constant, the average velocity between time 0 and t is vi+ (1/2)at and you multiply that by t to get the distance moved. Add that to initial distance (from the reference point) and you get the new distance.

"and this formula, which i don't know what it's used for at all, but i know it's important:
Vf^2 = Vi^2 +2ad (d= distance traveled)"

I presume Vf is the "final velocity", Vi is the "initial" or starting velocity. The advantage of this is that you can calculate the final velocity if you know the distance but not the time.

For example if the constant acceleration is 2 m/sec2, vi is 1 m/s and t= 4 seconds, the final velocity, vf will be 1+ 2(4)= 9 m/s. The distance moved will be (using d= vit+ (1/2)at2) d= 1(4)+ (1/2)(2)(16)= 4+ 16= 20.
Vf2= 92= 81 m2/sec2
Vi2= 12= 1 m2/sec2
2ad= 2(2)(20)= 80
The formula would give 81= 1+ 80 (m2/sec2)which is certainly true.

If we were told that the initial velocity was 1 m/s, acceleration 2 m/sec2, but that the acceleration lasted for 20 m rather than 4 seconds, we would calculate vf2= 1+ 80= 81 and so find that the final velocity was 9 m/s without needing to know the time.
 
  • #3
thank you sooo much, everything makes sense now
 

1. What is the formula for constant velocity?

The formula for constant velocity is distance divided by time, or v=d/t. This means that the velocity remains the same throughout the entire period of motion.

2. How is constant velocity different from average velocity?

Constant velocity refers to an object moving at the same speed and direction, while average velocity takes into account any changes in the velocity over time. In other words, constant velocity is the actual velocity of the object, while average velocity is an average of all the velocities during the motion.

3. Can the constant velocity formula be used for any type of motion?

Yes, the constant velocity formula can be used for any type of motion where the velocity remains unchanged. This includes linear motion, circular motion, and any other type of motion where the speed and direction remain the same.

4. How do I solve for distance or time using the constant velocity formula?

To solve for distance, you would multiply the velocity by the time, or d = v*t. To solve for time, you would divide the distance by the velocity, or t = d/v. Make sure to use consistent units for both distance and time, such as meters and seconds.

5. Are there any limitations to using the constant velocity formula?

The constant velocity formula assumes that there are no external forces acting on the object, such as friction or air resistance. It also assumes that the velocity remains constant throughout the entire period of motion. If these assumptions are not met, then the formula may not accurately represent the motion of the object.

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