Uniform Linear Motion

Motion Without Changing Velocity

Uniform linear motion is motion along a straight path with constant velocity. Constant means the speed stays the same and the direction also does not change.

Picture a small rail cart moving on a straight track. If it moves $2\text{ m}$ every $1\text{ s}$ , then does the same thing in the next second, the motion is uniform linear motion.

In uniform linear motion, the object may keep moving. What stays unchanged is its velocity.

\begin{aligned} \Delta x &= vt \\ x_t &= x_0+vt \end{aligned}

The symbol $x_0$ means initial position, $x_t$ means position after time $t$ , $v$ means velocity, and $\Delta x$ means displacement.

Position Marks With Equal Spacing

If an object's position is recorded at equal time intervals, uniform linear motion produces equally spaced marks. This is like a ticker tape: marks are made regularly, so the gaps between marks show how far the object moves during each time interval.

Suppose the initial position is $x_0=1\text{ m}$ and the velocity is $+2\text{ m/s}$ . That means the position increases by $2\text{ m}$ every second.

Time	Position
$0\text{ s}$	$1\text{ m}$
$1\text{ s}$	$3\text{ m}$
$2\text{ s}$	$5\text{ m}$
$3\text{ s}$	$7\text{ m}$
$4\text{ s}$	$9\text{ m}$
$5\text{ s}$	$11\text{ m}$

The equal part is the difference between positions, not the position value itself. From $1$ to $3$ , from $3$ to $5$ , and so on, the difference is always $2\text{ m}$ .

Uniform Motion Car Marks

Change the constant velocity to see the distance between marks stay equal every second.

Constant velocity: $4\text{ m/s}$
Mark interval: $1\text{ s}$
Distance between marks: $4\text{ m}$
Motion time: $5\text{ s}$

Calculating Final Position Without Guessing

Suppose an object starts from $x_0=1\text{ m}$ and moves right with constant velocity $v=2\text{ m/s}$ for $5\text{ s}$ . Its displacement is:

\begin{aligned} \Delta x &= vt \\ &= 2(5) \\ &= 10\text{ m} \end{aligned}

Its final position is:

\begin{aligned} x_t &= x_0+\Delta x \\ &= 1+10 \\ &= 11\text{ m} \end{aligned}

This calculation works because the velocity does not change. If the velocity changes, we cannot use one fixed value of $v$ for the whole motion.

Recognizing Uniform Motion on Graphs

Uniform linear motion is easy to recognize from two basic graphs. The velocity-time graph shows whether velocity changes, while the position-time graph shows how position increases.

Graph	Shape in uniform linear motion	Meaning
Velocity against time	Horizontal line	Velocity is constant
Position against time	Slanted straight line	Position changes regularly

The area under a velocity-time graph equals displacement. For uniform linear motion, that area is a rectangle, so $\Delta x=vt$ .

On a position-time graph, the slope of the line represents velocity. A steeper line means a larger velocity. For uniform linear motion, the line stays straight because the slope does not change from start to finish.

Constant Speed Is Not Always Constant Velocity

Uniform linear motion needs constant velocity, not only constant speed. Speed only tells the size of the motion, while velocity tells both size and direction.

A car moving with constant speed on a circular road is not in uniform linear motion, because the direction of its velocity keeps changing. A rail cart moving straight with constant speed and direction is in uniform linear motion.