Newtonian mechanics
Position, velocity, acceleration
Position tells where an object is; velocity describes how quickly and in which direction position changes; acceleration describes how velocity changes.
Track an object along a line: position answers “where?”, while velocity and acceleration describe how its motion changes over time.
Definition: Quantities and model
Choose an origin and positive direction before recording position x. Signed velocity gives direction; its magnitude is speed. Acceleration in the direction of velocity can increase speed, while acceleration opposite to it can reduce speed.
Reading the model
Position tells where an object is; velocity describes how quickly and in which direction position changes; acceleration describes how velocity changes.
Example: Worked example
A cart moves from x₁ = 2 m to x₂ = 14 m in 4 s. Its average velocity is (14 − 2)/4 = 3 m/s in the positive direction.
Solution
A cart moves from x₁ = 2 m to x₂ = 14 m in 4 s. Its average velocity is (14 − 2)/4 = 3 m/s in the positive direction.
On a straight road, choose a positive direction and an origin so signs have meaning. If a bicycle is at 0 m at 0 s and at 24 m after 6 s, its average velocity is 4 m/s; motion opposite the chosen direction has negative velocity. Average acceleration is the velocity change divided by time, so a change from 2 to 8 m/s in 3 s gives 2 m/s².
Example: From velocity to acceleration
A car speeds up from 3 m/s to 9 m/s in 3 s. Find its average acceleration.
Solution
a=(9−3)/3=2 m/s².
When reading measurements, distinguish position at an instant from distance traveled. Velocity has direction, while speed is its magnitude; acceleration describes a change in velocity, not simply fast motion. A slowing object accelerates opposite to its velocity.
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