1.3 - Acceleration

The formula for acceleration

Where:

• $a$ = Acceleration, in metres per second squared (m/s²)
• $v$ = Final velocity, in metres per second (m/s)
• $u$ = Initial velocity, in metres per second (m/s)
• $t$ = Time taken, in seconds (s)

The change in velocity is the final velocity minus the initial velocity ($v-u$).

Worked example - Time for a given acceleration

A cyclist accelerates at 1.5 m/s² from 3.0 m/s to 7.5 m/s. Find the time it takes to do this.

Free fall and the acceleration of free fall

• In the absence of air resistance, all objects fall at the same rate regardless of their mass.
• An object dropped from rest speeds up as it falls - its speed increases by about 10 m/s every second.
• The steady acceleration of an object falling freely from rest is called the acceleration of free fall, g. Near the Earth's surface its value is about 10 m/s².

Vertical motion under gravity

• When a body is thrown straight up, gravity opposes its motion.
• Its velocity decreases by about 10 m/s each second until, at the top of its path, its velocity is zero.
• This is a negative acceleration, also called a deceleration or retardation, of about 10 m/s².

Example - Ball thrown straight up at 50 m/s

• Initial velocity: u = 50 m/s.
• At the top of its path: v = 0 m/s.
• It loses 10 m/s each second, so it loses all 50 m/s after 5 seconds.