# Acceleration equation with unknown final velocity

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I was looking for the equation for acceleration, and I found this webpage:

However, this equation doens't help me, because in my current situation, I don't know the final velocity.

I know the starting velocity was 0 m/s, because the object whose acceleration I'm trying to calculate started in a stationary position.

What's the equation for figuring out the acceleration if you begin at rest, and then traverse d meters over the course of t seconds? Obviously, the AVERAGE velocity would be d/t, but how do I calculate the acceleration?

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If the acceleration is contstant, the average velocity is half the final velocity.

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The acceleration would be the second derivative of the distance with respect to time, which is written as

d2s/dt2

Where s is distance and t is time

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Ok, hypothetical scenario:

If I'm in a parked car, and then I step on the gas, traveling the hypotnuse of a 100m x 100m right triangle in 10 seconds, then I'd be traveling a straight distance of 141.42 meters, right?

So, if I do so in 10 seconds, then my average speed is 14.14 m/s, right?

So, you're saying that my final velocity is 28.28 m/s?

So, that would mean that my average acceleration would be 2.83 m/(s^2)?

The acceleration would be the second derivative of the distance with respect to time, which is written as

d2s/dt2

Where s is distance and t is time

So, what's the d stand for?

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d would be for the derivative. If you had a function f(x) which is the same as y, then you could write the derivative 2 ways. One is f'(x). The second is dy/dx.

With the second derivative, you could also write it 2 ways. One is f''(x). The other is d2y/dx2

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I think that you need to find a better website, that one was rather elementary.

Science Forums is a good one

If

u is the initial velocity

v is the final velocity

s is the distance travelled

t is the time is the time of travel

f is the acceleration, which must be constant throughout t

There are several equations to choose from when doing these problems.

v = u +ft

v2 = u2+ 2fs

s = ut + 1/2 ft2

s = vt - 1/2 ft2

s = 1/2(v+u)t

Remember that deceleration is negative acceleration ie f is negative for deceleration.

Edited by studiot
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I was looking for the equation for acceleration, and I found this webpage:

However, this equation doens't help me, because in my current situation, I don't know the final velocity.

I know the starting velocity was 0 m/s, because the object whose acceleration I'm trying to calculate started in a stationary position.

What's the equation for figuring out the acceleration if you begin at rest, and then traverse d meters over the course of t seconds? Obviously, the AVERAGE velocity would be d/t, but how do I calculate the acceleration?

d = 1/2 at2 if the acceleration is constant and it starts at rest. Thus, a = 2d/t2

This is from the basic kinematics equation s = v0t + 1/2 at2 which you get by taking a = dv/dt integrating twice (also using v = ds/dt).

If acceleration is not constant, then you don't have enough information to solve the problem.

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