**Example 1**

An object accelerates over a period or 5 seconds from 2ms ^{-1} to 6ms ^{-1}

How far does it travel during this time?

- u = 2ms
^{-1} - v = 6ms
^{-1} - t = 5s
- s = ?

Use equation (1)

s = (v + u)/2 x t

s = (6+2)/2 x 5 = **20m**

**Example 2**

An object reaches a final velocity of 120ms ^{-1} after accelerating at a rate of 5ms ^{-2} for 1 minute

What was its initial velocity?

- u = ?
- v = 120ms
^{-1} - t = 1min = 60s
- a = 5ms
^{-2}

Use equation (2)

v = u + at Therefore u = v -at

u = 120 - 5 x 60 = **-180ms ^{-1}**

**Example 3**

An object that is initially travelling at 4ms^{-1}accelerates at a rate of 2ms ^{-2} over a period or 7 seconds

How far does it travel during this time?

- u = 4ms
^{-1} - a = 2ms
^{-2} - t = 7s
- s = ?

Use equation (3)

s = ut + ^{1}/_{2}at^{2}

s = 4 x 7 + ^{1}/_{2} x 2 x 7^{2} = **77m**

**Example 4**

An plane lands on a runway with an initial velocity of 100ms ^{-1} and the maximum acceleration produced by the brakes is
-5ms ^{-2} (note the acceleration due to the breaks is opposite to the direction of velocity!)

What is the minimum length of runway needed for the plane to come to rest?

- u = 100ms
^{-1} - v = 0 ( we want the plane to stop!)
- a = -5ms
^{-2} - s = ?

Use equation (4)

v^{2} = u^{2} + 2as Therefore s = (v ^{2} - u ^{2})/2a

s = 0 - 100 ^{2}/(2 x (-5)) = **1000m** (1km)