When the velocity of a particle changes with time, the particle is said to be accelerating. For example, the velocity of a car increases when you step on the gas and decreases when you apply the brakes. It is easy to quantify changes in velocity as a function of time in exactly the same way we quantify changes in position as a function of time.
In the following example, we will see how the velocity of a particle changes while the particle is moving. Suppose a particle moving along the x axis has a velocity $v_{xi}$ at time $t_i$ and a velocity $v_{xf}$ at time $t_f$.
The average acceleration of the particle is defined as the change in velocity $\Delta v_x$ divided by the time interval $\Delta t$ during which that change occurred: $$ a = {{\Delta v_x} \over {\Delta t}}$$ The SI unit of acceleration is meters per second squared $(m/s^{2})$.
It might be easier to interpret these units if you think of them as meters per second per second. For example, suppose an object has an acceleration of $2 m/s^2$. You should form a mental image of the object having a velocity that is along a straight line and is increasing by 2 m/s during every 1-s interval. If the object starts from rest, you should be able to picture it moving at a velocity of $+2 m/s$ after $1 s$, at $+4 m/s$ after $2 s$, and so on. In some situations, the value of the average acceleration may be different over different time intervals. It is therefore useful to define the instantaneous acceleration as the limit of the average acceleration as $\Delta t$ approaches zero.
Acceleration Related Questions