# Average acceleration formula

## Average acceleration formula

The Average acceleration formula can be explained as average velocity divided by average time. Very often, the velocity of a particle changes either in magnitude, in direction, or both as the motion proceeds. The body is then said to have an acceleration. The acceleration is defined as the time rate of change of velocity. The average acceleration is defined as

The direction of average acceleration (vector) is the direction of change in velocity (vector). Its unit is m/s2.

The instantaneous acceleration is defined by

In general, there is no relation between the direction of velocity vector and the direction of acceleration vector.

### Example

The position of a particle is given by X = 40 – 5t– 5t2, where x is in more and t is in second

(a) Find the average velocity between 1 and 2s

(b) Find its instantaneous velocity at 2s

(c) Find its average acceleration between 1 and 2s

(d) Find its instantaneous acceleration at 2s

Solution: (a) At   t = 1s; xi 30 m

t = 2s; xt = 10 m

(b) V = dx/dt

= -5-10t

At t = 2s;

v = – 5-10(2)

= -25 m/s

(c) At t = 1s; v = –5–10(1) = –15 m/s

t = 2s; v = –5–10(1) = –25 m/s

(d) a = dv/dt

= -10m/s2