# S-Cool Revision Summary

## S-Cool Revision Summary

**If acceleration is constant**, a quicker way than drawing graphs to find acceleration, velocity or displacement is to use some equations.

The symbols for displacement, initial velocity, etc. are shown on the diagram.

## Projectiles

**Vectors** at right angles to one another are independent.

If you are considering the effect of two (or more) vectors on an object, it is important to remember that:

**Vectors at right angles to each other do not have any effect on each other.**

*An easy example:* no matter how hard you push down on an object, you will never make it accelerate sideways.

**Projectile Motion - ignoring friction**

If a stone is thrown horizontally from a cliff top it follows what is called **projectile motion.**

**Vertically** it has constant acceleration downwards (due to gravity).

**Horizontally** it has constant velocity (for instance, no acceleration or deceleration if there is no friction).

*Some useful tricks:*

To find out about the ball at the highest point in its flight, remember that at that point vertically: v = 0 m/s.

(For that instant it is travelling horizontally so it has no vertical velocity at all).

To find the time for the whole flight you usually have to find the time for half the flight by considering the time for the vertical velocity to reduce to zero from its initial value (for instance, the time it takes the ball to stop moving any higher) and then double it.

## What if velocity and acceleration are in opposite directions?

**Direction is important**

To show different directions we use a positive or negative sign. It doesn't matter whether you choose up or down, left or right as positive, as long as you stick to it for the rest of the question.

*For example:*

If you are going to the right at 10ms^{-1} but accelerating to the left (for instance, decelerating) at 2ms^{-2}, then u = +10ms^{-1} and a = -2ms^{-2}

**Acceleration due to gravity**

Objects in a gravitational field experience a downward force, their weight. If unbalanced, this will produce a downward acceleration. This crops up frequently in A-level questions. However, it's easy to deal with. Simply always use acceleration as:

a = g = 9.81 ms^{-2} downwards.

*For example:*

Drop a stone from a cliff.

Initially, t = 0, u = 0, and a = + 9.81 ms^{-2} (*Note:* I've chosen down to be positive here)

Or

Throw a stone upwards at 10 ms^{-1}

Initially, t = 0, u = 10ms^{-1} and a = g = -9.81ms^{-2}. (*Note:* I've chosen up to be positive here to show that it doesn't matter which one you choose as long as you're consistent.)

## Equations

*Equations of Motion*

Learn to derive and use

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

v = u + at

s = ut + ½ at^{2}

## Symbols

s = displacement

u = initial velocity

v = final velocity

a = acceleration

t = time

g = acceleration due to gravity, 9.81 ms^{-2}