Fisica

Uniform Motion: Solved Exercises and Formula

Solve uniform (constant-velocity) motion problems step by step with s = s₀ + v·t and practise with five solved, verified exercises, from easy to advanced.

Recommended for: Grade 9 · Grade 10

In uniform motion an object moves along a straight line at constant velocity: its equation of motion is s = s₀ + v · t. If it starts from the origin (s₀ = 0) this becomes simply s = v · t, from which you also get v = s / t and t = s / v.

The three formulas you need

Every uniform-motion problem revolves around the relation s = v · t. Depending on what you need to find, you rewrite it in one of three forms: s = v · t for distance, v = s / t for speed, t = s / v for time. The only rule is to use consistent units: metres and seconds together, or kilometres and hours together.

Watch the units

The most common mistake is mixing km/h and m/s. To go from km/h to m/s, divide by 3.6; to go back, multiply by 3.6. Before you plug numbers into the formula, always check that distance, speed and time are expressed in compatible units.

Reading the graph

In uniform motion the position–time graph is a straight line, and its slope is exactly the velocity: a steeper line means a faster object, a horizontal line an object at rest. In the exercises below you will find the same idea at increasing difficulty, from a direct distance calculation to two objects meeting. Every result is checked by recomputing it.

Solved exercises

1. A car travels at a constant speed of 20 m/s for 15 s. How far does it go? base

Show solution
  1. Uniform motion means s = v · t.
  2. Substitute the data: v = 20 m/s, t = 15 s.
  3. s = 20 · 15 = 300.

Answer: s = 300 m

2. A cyclist covers 120 m in 8 s at constant speed. What is their speed? base

Show solution
  1. From s = v · t, solve for speed: v = s / t.
  2. Substitute: v = 120 / 8.
  3. v = 15.

Answer: v = 15 m/s

3. A train travels at a constant 30 m/s. How long does it take to cover 4.5 km? intermedio

Show solution
  1. Put everything in the same units: 4.5 km = 4500 m.
  2. Solve for time: t = s / v = 4500 / 30.
  3. t = 150 s, i.e. 2 min 30 s.

Answer: t = 150 s

4. A car travels at 90 km/h. Convert this to m/s and find how far it goes in 12 s. intermedio

Show solution
  1. Convert km/h to m/s by dividing by 3.6: 90 / 3.6 = 25 m/s.
  2. Apply s = v · t with v = 25 m/s and t = 12 s.
  3. s = 25 · 12 = 300.

Answer: v = 25 m/s ; s = 300 m

5. Two cyclists start at the same moment from two towns 300 m apart and ride toward each other along a straight road: the first at 6 m/s, the second at 4 m/s. After how long do they meet, and how far has each ridden? avanzato

Show solution
  1. They approach each other at a relative speed equal to the sum of the two: 6 + 4 = 10 m/s.
  2. Time to close the 300 m gap: t = 300 / 10 = 30 s.
  3. Distance of the first: s₁ = 6 · 30 = 180 m.
  4. Distance of the second: s₂ = 4 · 30 = 120 m.
  5. Check: 180 + 120 = 300 m, exactly the starting distance.

Answer: t = 30 s ; first 180 m, second 120 m

FAQ

What is the difference between uniform motion and uniformly accelerated motion?

In uniform motion the velocity is constant and the acceleration is zero, so the position–time graph is a straight line; in uniformly accelerated motion the velocity changes at a constant rate and the distance grows like a parabola.

How do you convert km/h to m/s?

Divide the value by 3.6, because 1 km/h equals 1000 m travelled in 3600 s. To go the other way, from m/s to km/h, multiply by 3.6.

What does the position–time graph of uniform motion look like?

It is a straight line whose slope equals the velocity: the steeper it is, the faster the object moves. The velocity–time graph, on the other hand, is a horizontal line.