PhysicsIntroductory PhysicsHigh school

Kinematics

Displacement, velocity and acceleration; constant-acceleration equations and projectiles.

Kinematics describes motion without asking what causes it. Position, displacement, velocity and acceleration are the core quantities. Displacement and velocity are vectors, so direction matters: walking 5 m east and then 5 m west covers 10 m of distance but zero displacement.

For constant acceleration, four equations connect displacement $\Delta x$ , initial velocity $v_0$ , final velocity $v$ , acceleration $a$ and time $t$ . Choosing the equation that omits the quantity you neither know nor need is the whole trick. Free fall near Earth is constant acceleration with $a = -9.8$ m/s² when up is positive.

Key terms

Constant-acceleration velocity: Velocity grows linearly with time.
$v = v_0 + at$
Constant-acceleration position: Displacement under constant acceleration.
$\Delta x = v_0 t + \tfrac{1}{2}at^2$

Key ideas

$v = v_0 + at$ ; $\Delta x = v_0 t + \frac{1}{2}at^2$ ; $v^2 = v_0^2 + 2a\Delta x$ ; $\Delta x = \frac{v_0 + v}{2}t$ .
Pick a positive direction and keep signs consistent.
On a position-time graph slope is velocity; on a velocity-time graph slope is acceleration and area is displacement.
Projectile motion: treat horizontal (constant velocity) and vertical (free fall) separately.

Worked example

A car accelerates from rest at $3$ m/s² for $6$ s. How fast is it going and how far has it travelled?

$v = 0 + 3 \times 6 = 18$ m/s.
$\Delta x = 0 + \frac{1}{2}(3)(6^2) = 54$ m.
Check with $v^2 = 2a\Delta x$ : $324 = 2 \times 3 \times 54$ .

Answer: $18$ m/s after $54$ m

Common mistakes

Mixing up distance and displacement.
Using $a = 9.8$ with up as positive.
Applying constant-acceleration equations when acceleration changes.

Practice questions

Try each one, then open the answer. Numerical answers on this page are verified by an automated calculation check.

1.A ball is dropped from rest. How fast is it falling after 2 s (use $g = 9.8$ )?
Show answer
$19.6$ m/s
2.A cyclist slows from 12 m/s to 4 m/s in 4 s. What is the acceleration?
Show answer
$-2$ m/s²
3.How far does an object fall from rest in 3 s?
Show answer
$44.1$ m

Keep practising

Quizzes and flashcards

Flashcards: Physics: Kinematics and Forces