Constant acceleration equations
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To derive the constant acceleration equations, we will need the following free fall equations.
v = v0 + g × tRemember that g is the acceleration of gravity and it is a constant acceleration. It is not only gravity that can give a constant acceleration. A car can drive also with a constant acceleration. We can generalize the two equations above by replacing g with a.
a is this case is any constant acceleration.
v = v0 + a × t equation 1
Derivation of more constant acceleration equations
We can use the equations above to get 3 more constant acceleration equations. To derive the constant acceleration equations, concepts of factoring, simplifying exponents, and fractions will be used.
Solve for t in equation 1
v = v0 + a × tv - v0 = a × t
Rewrite equation 2
2d = 2v0 × t + at2 (equation a)
Replace t in equation a
|
2d = 2v0
v - v0
a
|
+ a
(v- v0)2
a2
|
|
2d = 2v0
v - v0
a
|
+
(v- v0)2
a
|
|
2d = 2v0
v - v0
a
|
+ a
(v- v0)2
a2
|
|
2d = 2v0
v - v0
a
|
+
(v- v0)2
a
|
v2 - v02 = 2ad
v2 = v02 + 2ad equation 3
Solve for a in equation 1.
v = v0 + a × tv - v0 = a × t
Equation 2 can also be rewritten as
Replace a in the latter equation 2
|
d = v0t +
v - v0
t
|
×
t2
2
|
Replace a in the latter equation 2
|
d = v0t +
v - v0
t
|
×
t2
2
|
Finally, solve for v0 in equation 1 and replace v0 in equation 2.
v0 = v - at
We then have five important constant acceleration equations
Any questions about how I derive the constant acceleration equations, send me an email.