Position, Path Length, and Displacement
For one-dimensional motion, displacement over an interval is Delta x = x_f - x_i and may be positive, negative, or zero. Distance is the non-negative path length, so distance is always at least |Delta x|.
Why this shows up in the exam
Trips with reversals · Circular-path questions reduced to endpoint separation · Checking whether a particle returned to its start
Learn the idea
Position locates a particle, path length counts its route, and displacement compares only the endpoints. An odometer remembers every part of a journey, while displacement acts like an arrow drawn directly from the starting point to the finishing point. Returning to the start can therefore give a large distance but zero displacement.
🧠 Memory hook: Distance follows the road; displacement joins the endpoints.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Delta x = x_f - x_i — signed displacement from initial to final coordinate
- distance >= |Delta x| — path length cannot be smaller than endpoint separation
How to approach it
- 1Mark initial and final coordinates
- 2Compute signed endpoint change
- 3Add every path segment separately only when distance is asked
Common slip-ups that cost marks
- •Treating distance as signed
- •Using path length for displacement
- •Forgetting that zero displacement need not mean no motion
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A particle has initial speed 2 m/s and constant acceleration 3 m/s^2 for 4 s. What distance does it cover?
More from Kinematics
Distance, Displacement, Speed, and Velocity
Understand the differences between distance and displacement, and between speed and velocity, including how to calculate average speed and average velocity in various scenarios.
Equations of Motion and Uniform Acceleration
Learn the kinematic equations for uniformly accelerated motion, including applications to free fall, retardation, and calculation of distance in specific time intervals.
Projectile Motion
Study the motion of projectiles, including the independence of horizontal and vertical components, trajectory equations, maximum height, and the effect of initial conditions.
Relative Velocity and Motion Analysis
Explore how to determine the velocity of one object relative to another and analyze motion from different reference frames, including periodic motion.
Speed and Velocity
Instantaneous velocity is the signed rate v = dx/dt, while instantaneous speed is |v|. In one dimension the sign of v identifies motion along or opposite the positive axis.
Average Speed and Average Velocity
Over elapsed time Delta t, average speed equals total distance/Delta t and average velocity equals Delta x/Delta t. For equal distances the relevant mean of speeds is harmonic, not arithmetic.