Equations for uniform acceleration

When we’re working with calculations involving motion, we’re usually working with 3-4 of these 5 values:

• displacement or distance, s
• initial velocity or speed, u
• final velocity or speed, v
• acceleration, a
• time, t

The equations

If we know 3 of these values, we can work out the other 2 using these equations:

v=u+at

s=\frac{u+v}2\times t

s=ut+\frac12at^2

s=vt-\frac12at^2

v^2=u^2+2as

Calculations

A car accelerates from rest at 2\text{ m/s}^2 for 5\text{ s}. How far does it go?

• u=0\text{m/s} (since it starts from rest)
• a=2\text{m/s}^2
• t=5\text{s}
• s=?
• Use s=ut+\frac12at^2 to find s
• s=0\times5+\frac12\times2\times5^2
• s=25\text{m}

A car accelerates from 10\text{ m/s} to 30\text{ m/s} in 4\text{ s}. What is its acceleration?

• u=10\text{ m/s}
• v=30\text{ m/s}
• t=4\text{ s}
• a=?
• Use v=u+at to find a
• a=\frac{v-u}t
• a=\frac{30-10}4
• a=5\text{ m/s}^2

A car accelerates from 20\text{ m/s} to 40\text{ m/s} over a distance of 300\text{ m}. How long does it take?

• u=20\text{ m/s}
• v=40\text{ m/s}
• s=300\text{ m}
• t=?
• Use v^2=u^2+2as to find a
• a=\frac{v^2-u^2}{2s}
• a=\frac{40^2-20^2}{2\times300}
• a=3.33\text{ m/s}^2
• Use v=u+at to find t
• t=\frac{v-u}a
• t=\frac{40-20}{3.33}
• t=6\text{ s}

A car accelerates from 15\text{ m/s} to 25\text{ m/s} in 10\text{ s}. How far does it go?

• u=15\text{ m/s}
• v=25\text{ m/s}
• t=10\text{ s}
• s=?
• Use s=\frac{u+v}2\times t to find s
• s=\frac{15+25}2\times10
• s=200\text{ m}

A car accelerates from 5\text{ m/s} to 25\text{ m/s} over a distance of 400\text{ m}. How long does it take?

• u=5\text{ m/s}
• v=25\text{ m/s}
• s=400\text{ m}
• t=?
• Use v^2=u^2+2as to find a
• a=\frac{v^2-u^2}{2s}
• a=\frac{25^2-5^2}{2\times400}
• a=1.25\text{ m/s}^2
• Use v=u+at to find t
• t=\frac{v-u}a
• t=\frac{25-5}{1.25}
• t=16\text{ s}

A car accelerates from 0\text{ m/s} to 20\text{ m/s} in 8\text{ s}. How far does it go?

• u=0\text{ m/s}
• v=20\text{ m/s}
• t=8\text{ s}
• s=?
• Use s=\frac{u+v}2\times t to find s
• s=\frac{0+20}2\times8
• s=80\text{ m}

A car accelerates from 10\text{ m/s} to 30\text{ m/s} over a distance of 200\text{ m}. How long does it take?

• u=10\text{ m/s}
• v=30\text{ m/s}
• s=200\text{ m}
• t=?
• Use v^2=u^2+2as to find a
• a=\frac{v^2-u^2}{2s}
• a=\frac{30^2-10^2}{2\times200}
• a=4\text{ m/s}^2
• Use v=u+at to find t
• t=\frac{v-u}a
• t=\frac{30-10}{4}
• t=5\text{ s}

A car accelerates from 20\text{ m/s} to 40\text{ m/s} in 6\text{ s}. How far does it go?

• u=20\text{ m/s}
• v=40\text{ m/s}
• t=6\text{ s}
• s=?
• Use s=\frac{u+v}2\times t to find s
• s=\frac{20+40}2\times6
• s=180\text{ m}