Speed and Velocity

"Speed is the rate at which an object changes its location. Like distance, speed is a scalar because it has a magnitude but not a direction." "$\Delta t = t_f - t_0.$" "Average speed, *v*_avg, is the distance traveled divided by the time during which the motion occurs." "Its speed at a specific instant in time, however, is its instantaneous speed. A car's speedometer describes its instantaneous speed." "Velocity describes the speed and direction of an object. ... Average velocity is displacement divided by the time over which the displacement occurs." "$\vec{v}_{\text{avg}} = \frac{\text{displacement}}{\text{time}} = \frac{\Delta\vec{d}}{\Delta t} = \frac{\vec{d}_f - \vec{d}_0}{t_f - t_0}$" "If your car's odometer shows the total distance traveled was 6 km, then your average speed was 12 km/h. Your average velocity, however, was zero because your displacement for the round trip is zero." "A student has a displacement of 304 m north in 180 s. ... $\vec{v}_{\text{avg}} = \frac{\Delta\vec{d}}{\Delta t} = \frac{304 \text{ m}}{180 \text{ s}} = 1.7 \text{ m/s north}$" "Layla jogs with an average velocity of 2.4 m/s east. ... $\Delta\vec{d} = \vec{v}_{\text{avg}} \, \Delta t = (2.4 \text{ m/s})(46 \text{ s}) = 1.1 \times 10^2 \text{ m east}$" "Phillip walks ... 428 m west with an average velocity of 1.7 m/s west? ... $\Delta t = \frac{\Delta\vec{d}}{\vec{v}_{\text{avg}}} = \frac{428 \text{ m}}{1.7 \text{ m/s}} = 2.5 \times 10^2 \text{ s}$"