The formulae for constant motion $v=u+at$ can be used to model an object moving vertically under gravity.

This is because all objects accelerate towards the earth at a constant rate, if you ignore air resistance.

On Earth, the acceleration due to gravity is represented as $g$ and is approx. $9.8ms^{-2}$ .

$g = 9.8ms^{-2}$

Example

A book falls off the top shelf of a bookcase. The shelf is 1.4 m above a wooden floor. Find: a the time the book takes to reach the floor, b the speed with which the book strikes the floor.

s = 1.4 (height) u = 0 (end velocity) a = 9.8 (gravity but +ve) t = ? s = u t + \frac{1}{2} a t^{2} 1.4 = 0 t + \frac{1}{2} 9.8 t^{2} 1.4 = \frac{1}{2} 9.8 t^{2} \frac{1}{2} 9.8 = \frac{1.4}{4.9} t^{2} = \frac{1.4}{4.9} = 0.5345 \dots

from the book

Remember

Vertical Motion Under Gravity

Example

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