Kinematics means describing motion without worrying (yet) about what causes it. If an object's acceleration is constant, a small set of equations lets you predict exactly where it will be, how fast it will go and how long it will take.
Explained simply
First, some careful vocabulary.
Displacement (s) is the straight-line distance from start to finish with a direction. Walk 5 m forward and 5 m back, and you have travelled 10 m but your displacement is zero.
Velocity is the rate of change of displacement, so it has a direction too.
Acceleration (a) is the rate of change of velocity.
These are vectors, meaning quantities with both size and direction. In one dimension, we handle direction with signs: pick one direction as positive, and anything going the other way is negative.
When acceleration is constant, five quantities are linked: s, u (initial velocity), (final velocity), and . These are the :
Watch it explained
Deriving the SUVAT Equations of Motion - A Level Physics
Physics Online
Using SUVAT Equations of Motion - GCSE & A-Level Physics
3The equations only work when acceleration is constant.
4In free fall near Earth, every object accelerates downwards at about 9.8 m/s², ignoring air resistance.
5For projectiles, treat horizontal and vertical motion separately.
v
a
t
suvat equations
v=u+at
s=2(u+v)t
s=ut+21at2
v2=u2+2as
Each equation leaves out one of the five quantities. The trick is to list what you know, spot what you need, and pick the equation that skips the quantity you do not care about.
Free fall is the classic case. Near Earth's surface, ignoring air resistance, everything accelerates downwards at g≈9.8 m s−2, whether it is a feather in a vacuum or a bowling ball.
For a projectile (something thrown through the air), the horizontal and vertical motions are independent. Horizontally there is no force (ignoring air), so velocity stays constant. Vertically it is free fall. Solve each direction on its own, connected only by the shared time.
Worked example
A ball is thrown straight up at 15 m/s. How high does it go, and how long does it take to reach the top? Take up as positive, so a=−9.8 m s−2.
What we know:u=15, v=0 (it stops for an instant at the top), a=−9.8.
Time to the top, using v=u+at:
0=15−9.8t⇒t=9.815≈1.53 s
Maximum height, using v2=u2+2as:
0=152+2(−9.8)s⇒s=19.6225≈11.5 m
By symmetry, it takes another 1.53 s to fall back, and it lands at 15 m/s downwards.
Velocity–time graph for a ball thrown up at 15 m/s: a straight line of gradient −9.8 m/s² crossing zero at 1.53 s (the top) and reaching −15 m/s at 3.06 s; the area above the axis (+11.5 m) equals the area below it (−11.5 m)
Common mistakes
Ignoring signs. If up is positive, gravity is −9.8. Mixed signs give nonsense answers.
Thinking acceleration is zero at the top. Velocity is zero at the top, but gravity is still pulling, so a is still −9.8.
Using suvat when acceleration changes, for example when air resistance is significant.
Mixing horizontal and vertical in projectile problems. Keep them in separate columns.
Where you see this in real life
Engineers use these equations to design the length of airport runways, based on how fast a plane can accelerate. Road safety experts calculate stopping distances from braking deceleration. Sports scientists analyse the flight of a long jumper or a basketball shot as a projectile. Accident investigators even work backwards from skid marks to estimate how fast a car was going before it braked.