How can you find initial velocity when the displacement is given but time is not?

Answer 1

Unfortunately, the question is so vague it can't be answered specifically. But I will use my intuition and say that you are a high-school student studying algebra-based physics and are now up to the chapter or unit on rectilinear motion. If so, read on. If not, well, then perhaps you could use the discussion page to add more info (and maybe rephrase the question). The general formula for straight-line motion is a quadratic equation. Displacement (or distance) is expressed as a function of time. In other words, dispacement is the dependent variable and time is the independent variable. But displacement is also dependent upon the values of initial displacement, initial velocity, and acceleration, which are all coefficients of the general displacement formula. Here is the formula: d = d0 + v0t + (1/2)at2, where d is the displacement, d0 is the initial displacement (in other words, the displacement at t = 0), v0 is the initial velocity (velocity at t = 0), and a is the acceleration. So, using the formula, you can solve for distance traveled (displacement) if you know the values of all those parameters to the right of the equal sign. But what if you don't know the value of t? Well, in that case, you had better know the values of all the other parameters, including the d to the left of the equal sign. If you know the initial distance, the total distance traveled, the initial velocity, and the acceleration, you can solve for t. Usually, we set up our frame of reference so that d0 = 0. Frequently, v0 = 0, also. (In other words, the object has no initial displacement and no initial velocity.) If you know the distance traveled, d, and the acceleration, a, then you can solve for t using the simplified formula d = (1/2)at2. Solving for t, you get t = SQRT(2d/a).Since you now know t and d, you can calculate the object's average velocity using the formula, va = d/t. Since the object started at rest (it had zero initial velocity), its final velocity, vf, is 2va. You might be able to use the equation of motion v2 = u2 + 2ad, where v is the final velocity, u is the initial velocity, a is the acceleration & d is the distance covered. Quite often the initial velocity is zero, so the equation simply becomes v2 = 2ad. So the final velocity v =SQRT(2ad).

Answer 2

You do need some data to find the acceleration.

You do need some data to find the acceleration.

You do need some data to find the acceleration.

You do need some data to find the acceleration.

Answer 3

Let's see if we understand this. You get a monster question on a Physics test,

and it says:

A body moving in a straight line started out at the speed of 'S' and accelerated

at the rate of 'A'. What was its speed after it covered the distance of 'D' ?

That's how we understand your question. Here's how we'd approach it:

At any time 'T', its speed is [ S + A T ].

Over that whole period of time, its average speed is

1/2 (original speed + final speed) = 1/2 (S + S + A T) = S + A T/2

The distance it covers during that time is

(average speed) x (time) = (S + A T/2) x (T) = 1/2 A T2 + S T

and the distance you're interested in is 'D'. After covering the distance of 'D',

D = 1/2 A T2 + S T . . . or . . . 1/2 A T2 + S T - D = 0

There's a nice, friendly quadratic equation, like hundreds you've solved before.

It looks scary at first, because there are so many letters in it, but there's only

one letter there that you don't know. You know A, S, and D, so you can put

numbers in for them. 'T' is the only number you don't know ... the time the

object took to cover the distance of 'D'. Solve the quadratic equation for 'T'.

You'll know how long it took, and then, knowing that the final speed is 'S T',

you'll also know the final speed.

Answer 4

One formula that can be used - assuming constant acceleration, of course! - is vf2 = vi2 + 2as, where vf is the final speed, vi is the initial speed, a is the acceleration and s is the distance. In your case, solve for final velocity.

Answer 5

Since you cannot use the time ... because it's not given ... you must use

the information that IS given, to calculate the initial velocity. It will most

likely include things like the final velocity, the acceleration, the change in

momentum, the change in kinetic energy, etc.

I can't tell you exactly how to do it, because I don't know what's given,

and even that could change from one problem to the next. But I can give

you the general approach, which will stand you in good stead no matter

what. The golden approach is:

Do not dwell upon that which is not given, but rather, turn

your attention, with gratitude, to that which is given.

Answer 6

If the displacement is given but the time is not, you can't directly calculate the initial velocity. The initial velocity would depend on how long it took to reach that displacement. You would need either the time or information about acceleration to determine the initial velocity.

Answer 7

Assuming you also know the final velocity and acceleration over the displacement then the initial velocity is

Vinitial = (Vfinal2 - 2*acceleration*displacement)0.5

Answer 8

You do need some data to find the acceleration.