Overview:

# Part 2: Projecting a particle directly upwards

## Constant acceleration formulae

You should be familiar with the constant acceleration or “suvat” formulae:

$$v=u+at$$

$$s=ut+\frac{1}{2}at^{2}$$

$$s=vt-\frac{1}{2}at^{2}$$

$$s=\frac{1}{2}\left(u+v\right)t$$

$$v^{2}=u^{2}+2as$$

## Weight

Remember, the weight of an object is the gravitational force exerted on the object. On earth, an object of mass $$m$$ kg experiences a force of $$mg \text{ N}$$ directed towards the centre of the earth, where $$g \approx 9.8 \text{ ms}^{-2}$$. The precise value of $$g$$ varies depending on latitude and altitude. Note the units of $$g$$: we have acceleration here. Any object that is under the influence of gravity alone (i.e. an object on which no other forces are being exerted) accelerates towards the centre of the earth at $$g \text{ ms}^{-2}$$. The mass of the object is irrelevant. If you release a feather and a bowling ball from the same height above the ground, they should hit the ground at the same time. Typically this won’t happen, because these objects aren’t under the influence of gravity alone; the objects experience air resistance, which has a greater impact on the feather. In a vacuum, however, we see that the two objects do indeed fall at the same rate:

## Splitting a velocity into perpendicular components

You should also be able to split a velocity into perpendicular components (most commonly into horizontal and vertical components):

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