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Equations of motion

When the acceleration is constant, speed, distance and time are linked by the equations of motion. You do not need all five quantities in every calculation. Write down what you know, see which quantity is missing, and choose the equation that does not contain it. The initial speed is the speed at the instant you call zero. From rest the initial speed is zero.

v = v_0 + at

speed after time t

s = v_0 t + \frac{1}{2}at^2

distance with constant acceleration

Symbols

$v_0$	initial speed	m/s
$v$	speed	m/s
$a$	acceleration	m/s²
$s$	distance	m
$t$	time	s

Example

A car starts from rest and accelerates at 2 m/s² for 8 s.

$v = 0 + 2 \cdot 8 = 16$ m/s and $s = \frac{1}{2} \cdot 2 \cdot 8^2 = 64$ m.

Check that the answer has the right unit, and that the speed increases when the acceleration and the time are positive.

Practise motion for free →

← Speed and acceleration · Free fall →

Part of Physics 1: Motion.