Uniform linear motion is motion at constant speed, like a car with cruise control on.
Acceleration is zero, so equal times mean equal distances, and distance is speed times time.
On a v-t graph the path is a horizontal line, and the area under it is the displacement.
Change speed and time and the object goes farther, and the area of the v-t graph changes.
What is Constant-Velocity Motion?
Before you write s=vt you have to check that speed is constant, which means acceleration is 0. If the net force is 0, Newton's first law gives that motion, and equal times add equal distances. When the v-t graph is a horizontal line, the rectangle under it is the displacement, which is why this lesson puts the formula and the area on the same page. If speed changes along the way, you cannot keep multiplying one v by t.
🚗 Intuition for Uniform Motion
①Imagine a car with cruise control on a highway
②Velocity does not change, so acceleration = 0
③It always covers the same distance over the same interval
④An x-t graph is a straight line whose slope is velocity
⑤Net force = 0 means uniform linear motion (Newton 1)
Visualizing Object Motion
5 m/s
4 s
seegongsik.com
A uniformly moving object travels along a number line
In the motion picture a circle sits on a horizontal scale at the position s=vt from the speed and time sliders. The speed arrow is drawn to match the chosen speed, and s=v×t is written underneath. In the v-t picture a rectangle under the horizontal line at that speed is filled, and that area is read as displacement s. Both pictures use the same speed and time. Change a slider and the circle, arrow, and rectangle are drawn again for those values; the circle does not run along the scale.
🔑 Key Observations
①Higher velocity → more distance in the same time
②Longer time → distance grows proportionally
③Distance = velocity × time — the most basic relation
v-t Graph and Displacement
These sliders are the same speed and time as the step above. Changing them here also moves the path and the v-t area.
5 m/s
4 s
seegongsik.com
Visualizing how the area under the v-t graph equals displacement
Uniform Motion Formula
s = vt
Distance (s) = velocity (v) × time (t)
A common mistake is to take round-trip average speed as the arithmetic mean of the two speeds. If the outward speed and the return speed differ, more time is spent on the slow leg, so the average is total distance divided by total time, and that value is smaller than the arithmetic mean. If speed changes along the way you cannot keep using one v in s=vt. Find each leg's distance and time first, then divide.
📊 Reading the v-t Graph
①Horizontal line on v-t graph = uniform motion (velocity unchanged)
②Area under the graph = distance (displacement)
③Rectangle area = base (t) × height (v) = vt = s
④The speed and time sliders are in Step 2. This graph moves with them
Worked Examples
Before you ask for a distance, check that speed is constant. If it is, use s=vt. If a train must clear a tunnel completely, take the distance as tunnel length plus train length and then use t=s/v. The train still has to travel its own length after the front exits. Only when speed is constant can you take time as distance divided by speed.
Example 1
A car travels at a constant 20 m/s for 5 seconds. How far does it go?
1
The problem says the speed is constant, so this is uniform motion. If speed changed along the way, one v times t would be wrong. That is why we use s = vt.
s = vt
2
Substitute v = 20 m/s and t = 5 s.
s = 20 × 5 = 100 m
▸ 100 m
Distance in uniform motion is speed × time, valid only when the speed is constant.
Example 2
A person walks the same path out at 4 m/s and back at 6 m/s. What is the average speed for the round trip?
1
Average speed = total distance ÷ total time. Let the one-way distance be d.
t = d4 + d6 = 5d12
2
Divide the total distance 2d by the total time.
v = 2d5d/12 = 245 = 4.8 m/s
▸ 4.8 m/s
Average speed is total distance ÷ total time, not the arithmetic mean (5 m/s). More time is spent on the slow leg, so it is below 5.
Summary
Once a=0, constant v, s=vt, and the horizontal v-t rectangle are in hand, the next lesson on uniformly accelerated motion has a baseline for what changes when speed is no longer constant. That an x-t graph is a straight line whose slope is speed then pairs with how the graph tilts when acceleration appears. Starting from a flat v-t makes the area of a tilted graph readable.
Uniform Linear Motion
s = vt, v = const, a = 0
Constant-velocity motion — distance is proportional to time
Average Speed
v = st
Total distance / elapsed time
exam-style
A 200 m long train moving at a constant 20 m/s passes completely through a 300 m tunnel. How long does this take?
①10 s
②15 s
③20 s
④25 s
⑤30 s
▸ ④ 25 s
1
To pass completely, the train must travel (tunnel length + train length).