Consider the graphic above. If we plot a graph of an object's motion under the influence of a constant force, we get a graph like the one above.
The initial velocity is u
The final velocity is v
The time of travel is 't'
and the distance travelled in that time is 's'
We get two relationships directly from that graph:
From the gradient we get:
equation 1
v = u + at
From the area under the graph we get
equation 2
s = 1/2 (u + v)t
If we replace the v in the second equation with the expression from the first. we get
s = 1/2 (u + (u + at))t = 1/2 (2u + at))t = (u + 1/2at)t
equation 3
s = ut + 1/2at2
If we square the first equation we get
v2 = (u + at)2= u2 + a2t2+ 2uat = u2 + 2a (1/2at2 + ut)
and substitution of (1/2at2 + ut) as 's' from equation 3 gives us:
equation 4
v2 = u2 + 2as
The thing to remember about these equations is they can only be applied to a situation in which a constant net force is acting.There has to be constant acceleration for them to apply.
Most examination questions wherein you have to use these equations will concern 'objects falling under gravity' - air resistance has to be negligible for them to be applicable... and you may be expected to state that air resistance is being ignored...
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