4.1.7

# Motion in a Straight Line

Test yourself

## Key Concepts of Motion

Displacement, speed, velocity and acceleration are fundamental concepts when describing motion in a straight line. You need to know how they link together.

### Displacement

• The displacement of an object, s, is the distance and direction from an object's starting position to its final position.

### Velocity and speed

• The velocity of an object, v, is the speed and direction an object is travelling.
• It is the rate of change of displacement:
• $v = \frac{\Delta s}{\Delta t}$
• Speed is the magnitude of the velocity.
• Instantaneous speed/velocity is the speed/velocity of an object at a given instant in time.
• Average speed/velocity is the total distance/displacement divided by the total time taken.

### Acceleration

• The acceleration of an object, a, is the rate (and direction) at which its velocity changes:
• $a = \frac{\Delta v}{\Delta t}$

### Delta symbol

• Delta, Δ, is the symbol meaning "change in".
• For example, Δs means change in displacement.

## Uniform Acceleration Equations

These four equations describe motion along a straight line with uniform (constant) acceleration or deceleration.

### Using the equations

• You will often be asked questions involving the 5 key concepts of motion in a straight line:
• s, displacement
• u, initial velocity
• v, final velocity
• a, acceleration
• t, time
• Usually you will be given three and asked to calculate a fourth using the 'suvat' equations, which are as follows...

### The equations

• $v = u + at$
• $s =(\frac{u + v}{2})t$
• $s = ut + \frac12 at^2$
• $v^2 = u^2 + 2as$