Motion in One Dimension

Constant Velocity

distance = speed x time

A cart moving at a steady speed travels a distance proportional to time. We track the units at every step and watch equal seconds map to equally spaced positions.

Example

A cart moving at a steady speed covers distance in proportion to time. We track the units and watch equal seconds map to equal spacing.

highlighted = computed this step

Read the motion

A cart moves at a constant speed of 3 metres per second for 4 seconds. We want the distance it travels.

v=3 m/s,t=4 sv = 3\ \text{m}/\text{s}, \quad t = 4\ \text{s}
A cart at the start of its motionA cart sits on a level track at the starting line with a velocity arrow pointing in the direction of motion.cartv

Choose the relationship

At constant velocity, distance is velocity multiplied by time. Check the units first: metres per second times seconds leaves metres, which is a distance.

x=v⋅tx = v \cdot t

Substitute the numbers

Put in the speed 3 and the time 4.

x=3 m/s ⋅ 4 sx = 3\ \text{m}/\text{s} \,\cdot\, 4\ \text{s}

Compute the distance

Multiplying gives 12 metres. Because the speed never changes, equal time steps cover equal distances.

x=12 mx = \hl{12}\ \text{m}
Equal time steps, equal spacing, equal arrowsSnapshots at each whole second sit at equally spaced marks with equal velocity arrows, because the speed never changes.t=0t=1t=2t=3cartv
mechanics The numbers here are deliberately small and clean so every step — including the unit check that turns metres-per-second times seconds into metres — can be read off exactly.