Does d = vt or 1/2(vi+vf)t?

Question

I am doing a Physics problem where the correct formula would be d = vt but as I look onto my formula sheet, d can also equal 1/2(vi+vf)t. When I plug in the numbers knot both equations, I get different answers for the d value. Can someone help me? Thank you in advance.

Answer 1

If the acceleration is constant, one can use the average velocity: v (bar) = (1/2)(vi + vf)

Answer 2

That would agree with Einstein addition of velocities equation if vf was the speed of light

Answer 3

The formula seem to be correct.

Write the distance traveled

d= 1/2 vi t+1/2 at t. Now at is the final velocity. a is the acceleration

d= 1/2 vi t+1/2 vf t= 1/2(vi+vf) t

Therefore, it is a correct formula.

Answer 4

d=vt is for a constant velocity.

1/2(vi+vf)t is for a constant acceleration when initial and final velocities are known.



1/2(vi+vt) is the average velocity. Thus you can replace it with v_avg, and then it looks the same as d=v t

Answer 5

Answer: yes

Answer: no

Answer: maybe

Answer: all three

Answer: none



You are one of those people who take one look at a formula without any kind of context or trying to look up what the formula is FOR and hope to solve a random problem using it, am I right?

That is something you obviously shouldn't be doing.



Displacement

d = 1/2(vi + vf)t is for uniform acceleration

It is intuitively obvious that if velocity is increasing at a constant rate, then the _average_ velocity is literally the arithmetic average of the starting and ending velocities so you use that one to find displacement.



d = vt for constant velocity (which is also a case of uniform acceleration, if you think about it, and is hence derived by putting vi = vf in the more general case)



For all other cases neither of the two apply.

Answer 6

Both are only a tiny part of the answer. In most cases NEITHER are accurate.



d = vt applies if the velocity is constant. ie the acceleration has a constant value of zero



d = 1/2 ( Vf+Vi) * t applies when the acceleration is constant ( it can be zero of course in which case Vf and Vi are the same so 1/2 (Vf+Vi)= 1/2 ( Vi + Vi) = 1/2 2 Vi = Vi)



Both of these are a subset of the more general

d = sum( Vi ) dt an integral sum of an infinite number of tiny time intervals. Each of which are infinitely short.



If you get different answers for both then Vf must be different from Vi so that you cannot use constant velocity



You EITHER have constant acceleration which is the second equation, or you have some more general acceleration so you need mathematics, calculus or, in the extreme case, a computer and numerical techniques.

Answer 7

Notice that if the velocity is constant, vi = vf. Is the 2nd formula invalid in that case? No, unnecessarily complicated but not invalid. See why:

d = 1/2(vi+vf)t

vi = vf ... so then just call either one v. And then if you substitute

d = 1/2(vf+vf)t = 1/2(2*v)t

d = vf*t

Answer 8

d = v * t



The equation above can only be used when the object’s velocity is constant.



d = ½ * (vi + v) * t



The equation above can only be used when the object is accelerating



d = vi * t + ½ * a * t^2



The following can also be used when the object is acceleration. Let’s assume the initial and final velocities are 10 m/s and 30 m/s. The time is 5 seconds.



d = ½ * (10 + 30) * 5 = 100 meters



a = (vf – vi) ÷ t

a = (30 – 10) ÷ 5 = 4 m/s^2



d = 10 * 5 + ½ * 4 * 5^2 = 100 meters



Let me show one equation that you can use to determine the distance if you do not know the time.



vf^2 = vi^2 + 2 * a * d

30^2 = 10^2 + 2 * 4 * d

8 * d = 800

d = 100 meters



I hope this will be helpful for you

Answer 9

Distance = velocity x time [ d= vt ]



or if a body is under a constant acceleration, you can take the average of the initial velocity [vi] and the final velocity [vf], which would be ½(vi + vf)

and multiply that by time to get the distance.