What are the SUVAT equations?
Four equations relating displacement, initial velocity, final velocity, acceleration and time under constant acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as; and s = ((u+v)/2)t. Knowing any three quantities gives the other two. The third is particularly useful because it contains no time — ideal when you know a distance but not how long it took.
What is the difference between speed and velocity?
Speed is how fast, velocity is how fast and in which direction. A car going round a roundabout at constant speed is continuously changing velocity, and is therefore accelerating even though the speedometer never moves. Acceleration is any change in velocity, which includes changes in direction — the point that makes circular motion possible.
Can acceleration be negative?
Yes, and negative simply means opposite to your chosen positive direction. It usually indicates slowing, but not always: an object thrown upward has constant downward acceleration throughout, including while it is still rising. Setting a consistent sign convention before starting is the single best way to avoid errors in these problems.
Do these equations work with changing acceleration?
No — they assume acceleration is constant. Free fall near the surface is a good approximation; a car accelerating through the gears is not, nor is anything with significant air resistance, because drag grows with speed. For varying acceleration you need calculus or numerical simulation. Applying SUVAT to a non-constant case is a common source of confidently wrong answers.
Why is it useful that displacement is not the same as distance?
Displacement is a vector — the straight line from start to finish — while distance is the total path travelled. Throw a ball up and catch it and the displacement is zero, though it clearly travelled some distance. SUVAT works in displacement, so an answer of zero is often correct rather than an error, and average velocity can be zero while average speed is not.
How do I choose which equation to use?
List what you know and what you want, then pick the equation containing exactly those and no others. If time is unknown and not wanted, v² = u² + 2as avoids it. If final velocity is neither known nor wanted, s = ut + ½at² is the one. Choosing well turns most problems into a single substitution rather than a chain of them.