Acceleration is the rate at which an object's velocity changes over time. Since velocity includes both speed and direction, acceleration can occur by changing speed, changing direction, or both. This means an object accelerates if it speeds up, slows down, or changes its direction of motion
. Acceleration is a vector quantity, meaning it has both magnitude and direction. It is mathematically defined as the change in velocity divided by the change in time:
a=ΔvΔt=v−v0ta=\frac{\Delta v}{\Delta t}=\frac{v-v_0}{t}a=ΔtΔv=tv−v0
where v0v_0v0 is the initial velocity and vvv is the final velocity over the time interval ttt
. Instantaneous acceleration is the acceleration at a specific moment, defined as the derivative of velocity with respect to time:
a=dvdta=\frac{dv}{dt}a=dtdv
Because velocity is the derivative of position with respect to time, acceleration can also be seen as the second derivative of position with respect to time
. Examples of acceleration include a car speeding up, a car slowing down, a planet orbiting the sun (changing direction), or an object falling under gravity
. In summary, acceleration measures how quickly and in what way an object's velocity changes, encompassing changes in speed and/or direction.
