# ACCELERATION

Some dragsters will reach 200 mph from rest in 3s
A family car can get to 60 mph from rest in 8s
An astronaut must be able to withstand very large changes of velocity at lift off
A sprinter will take a few metres of a 100m race to reach top speed
Test pilots experience large changes of velocity when turning at high speed
In a car crash you may stop in a very short time
When you hit a tennis ball its velocity is changed rapidly

All these are examples of CHANGES in the velocity of an object. It's actually a good thing to have a car that can change its velocity quickly, NOT so that you can reach 70 mph rapidly but so that you could over take quickly in an emergency.

We call the rate at which something can change its velocity the ACCELERATION of the object.

If the acceleration is positive the object is speeding up, if it is negative it is slowing down. We call this negative acceleration a DECELERATION or a RETARDATION.

Acceleration is the rate of change of velocity

Acceleration = change in velocity/time taken

Acceleration = [Final velocity - Initial velocity]/Time taken

Acceleration means an increase in velocity per second and so the units for acceleration are:

(metres per second) per second    written m/s2.

Our bodies experience a whole range of accelerations during our lives.
A family car may reach 3 m/s2 during acceleration, the acceleration of objects falling freely in the Earth's gravitational field is about 10 m/s2 and pilots of military jets may reach up to 50 m/s2.

However some animals can experience large accelerations, a perch may reach 33 m/s2, a bush baby 180 m/s2, a woodpecker 1000 m/s2 when pecking and when a flea jumps it may achieve 1400 m/s2! The acceleration of a rifle bullet in the barrel of the rifle will be at least 200 000 m/s2!

Example problems
1. A boy on a bike accelerates from 8m/s to 12m/s in 4s. Work out:
(a) his average velocity
(b) his acceleration

(a) average velocity = [12 + 8]/2= 10m/s
(b) acceleration = [12 – 8]/4 = 1 m/s2

2. A lady in a car travelling at 30m/s slows down steadily to a stop in 6s. What is her acceleration?

Acceleration = [0 – 30]/6 = - 5 m/s2
(Note the minus – she is slowing down)

Speed conversions
13.6 m/s (30mph) 22.7 m/s (50mph)
31.8 m/s (70mph) 45.5 m/s (100)mph

Problems
1. A girl reaches her top speed (8 m/s), 4s after the start of a 100m race. What is her acceleration?

2. A golf ball leaves the head of a golf club at 20 m/s, 0.2s after being hit from rest. What is the acceleration of the golf ball?

3. Work out the accelerations of the follwoing:
(a) a car changes its velocity from 15 m/s to 23 m/s in 2s
(b) A plane accelerates from 150 m/s to 250 m/s in 20 s
(c) A car travelling at 20 m/s brakes to a stop at some traffic lights in 4s