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| Motion under gravity - modelling with differentiation |
The motion of an object under gravity can easily be modelled by differentiation.
Suppose the motion of a stone is given by the formula, y = 16t - 4t2, where y and t are displacement and time respectively.
y = 16t - 4t2
dy/dt = 16 - 8t
When the stone reaches the highest point, dy/dt = 0
16 - 8t = 0
8t = 16
t = 2s
Maximum height reached by the stone = 16x2 - 4x22 = 16m
d2y/dx2 = -8 < 0
Therefore, when t = 2s, the height reaches the maximum.
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