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Equations of motion

When the acceleration is constant, four equations link the initial velocity, final velocity, displacement, acceleration and time. If you know three of the five quantities, you can find the other two by choosing the equation that leaves out the one quantity you neither know nor need.

v = v_0 + at

final velocity after time t

s = v_0t + \tfrac12 at^2

displacement

v^2 - v_0^2 = 2as

without time

Symbols

$v_0$	initial velocity	m/s
$v$	final velocity	m/s
$a$	acceleration	m/s²
$s$	displacement	m

Example

A car with $v_0 = 20$ m/s brakes at $a = -5.0$ m/s² to a stop. The braking distance is $s = \dfrac{v^2-v_0^2}{2a} = \dfrac{0-400}{-10} = 40$ m.

Pick the equation that leaves out the quantity you neither know nor are looking for.

Practise motion for free →

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Part of Foundations of Physics: Motion.