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The equations that quantitatively describes uniform acceleration motion are explained.
Let
a be the acceleration
u be the initial velocity at time t1
v be the final velocity at time t2
t = t 2 - t1
x is the displacement between t1 and t2
x0 is the initial position
The relationship between all the above quantities are given by the following equations:
definition of acceleration: a = (v - u) / t
| v = a t + u |
1 (deduced from above definition)
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| x = (1/2) a t 2 + u t + x0
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2 |
| x = (1/2)(u + v) t + x0
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3 |
| v 2 = u 2 + 2 a (x - x0)
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4 |
If x0 = 0 (start from origin) , the above equations simplifies to
| v = a t + u |
1
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| x = (1/2) a t 2 + u t |
2 |
| x = (1/2)(u + v) t |
3 |
| v 2 = u 2 + 2 a x
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4 |
If x0 = 0 (start from origin) and u =0 (starting from rest) the above equations simplifies further to
| v = at |
1
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| x = (1/2) a t 2 |
2 |
| x = (1/2) v t |
3 |
| v2 = 2 a x
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4 |
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