## Motion in a straight line with constant acceleration

Recall that acceleration at a given time measures the instantaneous change in velocity – see Quantities & Units in Mechanics. For motion in a straight line with constant acceleration, the speed along the line changes by the same amount every second. Hence, if speed is measured in metres per second (m/s) then acceleration is measured in metres per second per second (m/s/s). For example, consider a ball rolling along a flat surface:

If the ball rolls with speed 4 m/s and accelerates at a constant rate of 2 m/s/s, the ball will have speed 10 m/s after 3 seconds.

In general, for motion in a straight line with constant acceleration:

$\text{acceleration} = \frac{\text{change in velocity}}{\text{change in time}}\hspace{30pt}\text{or}\hspace{30pt}A=\frac{V-U}{T}$

where V is the final velocity, U is the initial velocity and T is the total time taken.

Rearranging gives the equation in an alternative form:

$V=U+AT$

Variable/Constant Description SI unit
S displacement m (metres)
U initial velocity m/s (metres per second)
V final velocity m/s (metres per second)
A acceleration m/s/s (metres per second per second)
T total time s (seconds)

These two equations are two of the SUVAT equations named so since they involve displacement (S), initial velocity (U), final velocity (V), acceleration (A) and time (T) for motion in a straight line with constant acceleration.