The average velocity is found by dividing the displacement (change in position) by the time interval during which the displacement occurs. The formula is:
vˉ=displacementtime=xf−xitf−ti\bar{v}=\frac{\text{displacement}}{\text{time}}=\frac{x_f- x_i}{t_f-t_i}vˉ=timedisplacement=tf−tixf−xi
where xfx_fxf and xix_ixi are the final and initial positions, and tft_ftf and tit_iti are the final and initial times. Alternatively, if the velocity changes at a constant rate, the average velocity can be calculated by taking the mean of the initial velocity uuu and final velocity vvv:
vˉ=u+v2\bar{v}=\frac{u+v}{2}vˉ=2u+v
Summary:
- Average velocity is a vector quantity expressing displacement per unit time.
- It is the slope of the position-time graph between two points.
- Formula using displacement and time: vˉ=xf−xitf−ti\bar{v}=\frac{x_f-x_i}{t_f-t_i}vˉ=tf−tixf−xi.
- Formula using initial and final velocity (constant acceleration): vˉ=u+v2\bar{v}=\frac{u+v}{2}vˉ=2u+v.
This gives a comprehensive way to find average velocity depending on the data available.
