Motion in One Dimension

Position and Velocity

how fast is it moving?

Velocity is how much position changes each second. We read two snapshots of a cart and divide the change in position by the elapsed time.

Example

Velocity is just how much your position changes each second. We read two snapshots of a cart and divide the change in position by the time.

highlighted = computed this step

Read the two snapshots

A cart is at 2 metres at the start and 8 metres after 3 seconds. How fast was it going?

xi=2 m,xf=8 mx_i = 2\ \text{m}, \quad x_f = 8\ \text{m}
A cart at its first and second positionsA cart shown at an earlier marked position and at its later position further along a level track.startcart

Find the change in position

Subtract the positions: 8 minus 2 is 6 metres.

Δx=8 m−2 m=6 m\Delta x = 8\ \text{m} - 2\ \text{m} = 6\ \text{m}

Find the elapsed time

The time taken is 3 minus 0, which is 3 seconds.

Δt=3 s−0 s=3 s\Delta t = 3\ \text{s} - 0\ \text{s} = 3\ \text{s}

Divide to get velocity

Velocity is change in position divided by time: 6 over 3 is 2 metres per second. The metres-over-seconds leaves metres per second. On a straight rightward track, this speed is just the size of the velocity.

v=ΔxΔt=6 m3 s=2 m/sv = \frac{\Delta x}{\Delta t} = \frac{6\ \text{m}}{3\ \text{s}} = \hl{2}\ \text{m}/\text{s}
The cart with its velocity arrowThe cart at its later position with an arrow showing how fast and which way it moves.cartv
mechanics Two clean positions and a whole number of seconds let us read the velocity off exactly, units and all.