Acceleration

Acceleration is derived from Δvelocity (in m s^-1) and Δtime (in s). This means we need to convert other units (km hr^-1 and min, for example) into SI units.

This is the same as:

a = Δv ÷ Δt

Δv = a × Δt

Δt = Δv ÷ a

On Graphs

On a d-t graph, acceleration looks like this:

Deceleration (negative acceleration) looks like this:

On a v-t graph, acceleration looks like B and D in the following graph. B is a higher rate of acceleration than D. Deceleration is represented by A (negative gradient). C is uniform motion (constant speed).

Calculating Acceleration from a Graph

To do this, you need a v-t graph. Acceleration is the gradient of the line on a v-t graph. This is the skill you are expected to be able to do to access Merit in NCEA. A v-t graph can also be used to calculate the distance covered (area under the line of the graph).

Alternatively, you use the tangent of the curved line for two points in a d-t graph (but this is very inaccurate). You then use this to find the initial and final velocity, and calculate acceleration from this. See Mr N if you really want to know how to do this!