Constant-Acceleration Equations
For constant signed acceleration a over an interval, v = u + at, s = ut + at²/2, v² = u² + 2as, and s = (u+v)t/2. These equations are not valid unchanged for variable acceleration.
Why this shows up in the exam
Uniformly accelerated vehicles · Straight-line launch and braking · Checking graph-derived results
Learn the idea
When acceleration is constant, a small set of equations links position, velocity, and time. Constant acceleration changes velocity by equal amounts in equal times. The average velocity is then the midpoint of the initial and final velocities.
🧠 Memory hook: Use only when a is constant, and keep every sign.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v = u + at — velocity after time t under constant acceleration
- s = ut + (1/2)at² — signed displacement in time t
- v² = u² + 2as — time-eliminated relation
- s = (u+v)t/2 — displacement from average velocity for constant acceleration
How to approach it
- 1Choose an axis and list signed u, v, a, s
- 2Select the equation omitting the unwanted variable
- 3Check whether reversal occurs inside the interval
Common slip-ups that cost marks
- •Using speed magnitudes where signed velocities are needed
- •Applying the formulas to variable acceleration
- •Mixing displacement with distance after reversal
🌟 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.
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|.
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.