Newtonian mechanics
Uniform linear motion
In uniform linear motion, an object travels along a straight line at constant velocity; distance grows in proportion to time.
A person walking steadily along a straight path covers equal distances in equal time intervals.
Definition: Quantities and model
x₀ is the initial position; v is the constant, signed velocity; x is the position after time t. If direction does not change, distance s = |v|t.
Reading the model
In uniform linear motion, an object travels along a straight line at constant velocity; distance grows in proportion to time.
Example: Worked example
A bicycle starts at x₀ = 5 m and travels in the positive direction at v = 3 m/s. After 4 s, x = 5 + 3×4 = 17 m.
Solution
A bicycle starts at x₀ = 5 m and travels in the positive direction at v = 3 m/s. After 4 s, x = 5 + 3×4 = 17 m.
The position–time graph for uniform straight-line motion is a straight line; its signed slope represents velocity. A person walking at 1.2 m/s for 25 s travels 30 m. For two people moving in opposite directions, assign one velocity a negative sign before calculating where they meet. Average velocity over a whole trip is not necessarily the instantaneous velocity at every moment.
Example: Walking distance
A person walks uniformly at 1.5 m/s for 40 s. How far do they travel?
Solution
s=vt=1.5×40=60 m.
For equal time intervals, constant velocity gives equal displacements. Convert units consistently before using the equation: 72 km/h is 20 m/s. The velocity–time graph is horizontal, while the position–time graph keeps a constant slope.
Quick check
Which quantity or statement is correct for this motion?
Which statement correctly describes the motion in this topic?
References
- Young, Freedman (2019). University Physics
- Halliday, Resnick, Walker (2014). Fundamentals of Physics