The three equations of motion
| Equation | Doesn't use |
|---|---|
| v = u + at | s |
| s = ut + ½at² | v |
| v² = u² + 2as | t |
| s = ½(u + v)t | a |
The trick is to pick the equation that leaves out the quantity you neither know nor need. The calculator does exactly that, and shows which one it used.
Only for constant acceleration. If the acceleration changes with time, you need calculus: a = dv/dt and v = ds/dt.
Distance in the nth second
sn = u + ½a(2n − 1). A classic JEE question: a body starting from rest covers distances in the ratio 1 : 3 : 5 : 7 in successive seconds.
For motion in two dimensions, try the projectile motion calculator.
Questions students ask
What are the three equations of motion?
v = u + at, s = ut + ½at² and v² = u² + 2as, for motion with constant acceleration.
How do I find the stopping distance of a car?
Use v² = u² + 2as with v = 0. For u = 20 m/s and a = −5 m/s², s = 400 ÷ 10 = 40 m.
Can displacement be negative?
Yes. It's a vector, so a negative value means the object ended up behind its starting point in the direction you called positive.