Acceleration is found by calculating the rate of change of velocity over time. The most common formula for acceleration is:
a=ΔvΔt=vf−vitf−tia=\frac{\Delta v}{\Delta t}=\frac{v_f-v_i}{t_f- t_i}a=ΔtΔv=tf−tivf−vi
where aaa is acceleration, vfv_fvf is final velocity, viv_ivi is initial velocity, tft_ftf is final time, and tit_iti is initial time. This formula essentially divides the change in velocity by the time over which the change occurred, yielding acceleration in units like meters per second squared (m/s²).
Here are key points about finding acceleration:
- You need to know the initial and final velocities of the object.
- You also need the initial and final times corresponding to those velocities.
- Subtract the initial velocity from the final velocity, and the initial time from the final time.
- Divide the velocity change by the time change.
Acceleration can be positive (speeding up) or negative (slowing down, often called deceleration). For example, if a car goes from 15 m/s to 35 m/s in 3 seconds, the average acceleration is:
a=35−153−0=203=6.66 m/s2a=\frac{35-15}{3-0}=\frac{20}{3}=6.66\text{ m/s}^2a=3−035−15=320=6.66 m/s2
If slowing down from 23.2 m/s to 0 in 1.5 seconds, acceleration is:
a=0−23.21.5−0=−15.47 m/s2a=\frac{0-23.2}{1.5-0}=-15.47\text{ m/s}^2a=1.5−00−23.2=−15.47 m/s2
This method applies generally to uniform acceleration situations.
