Kinematics

Five topics on motion in one, two, and three dimensions. Scalars and vectors in unit-vector notation, the calculus chain that ties position, velocity, and acceleration together through the derivative and its inverse, how each quantity shows up on a graph as a slope or an area, why the answer depends on who is watching, and how all of it carries over once an object moves in more than one direction at once.

Topics

1.1

Scalars and Vectors in One and Two Dimensions

Displacement, Velocity, and Acceleration

Representing Motion

Reference Frames and Relative Motion

Motion in Two or Three Dimensions

Lesson

Diag

locked

Equations For every problem in this unit

Velocity from time

$v_x = v_{x0} + a_x t$

Position from time

$x = x_0 + v_{x0}\, t + \tfrac{1}{2} a_x t^2$

Velocity from displacement

$v_x^2 = v_{x0}^2 + 2 a_x (x - x_0)$

Velocity, derivative of position

$v_x = \dfrac{dx}{dt}$

Acceleration, derivative of velocity

$a_x = \dfrac{dv_x}{dt} = \dfrac{d^2 x}{dt^2}$

Displacement, integral of velocity

$\Delta x = \displaystyle\int_{t_1}^{t_2} v_x\, dt$

Velocity change, integral of acceleration

$\Delta v_x = \displaystyle\int_{t_1}^{t_2} a_x\, dt$

Vector magnitude

$|\vec{r}| = \sqrt{x^2 + y^2}$

Pythagorean

$a^2 + b^2 = c^2$

Sine, opp / hyp

$\sin\theta = \dfrac{a}{c}$

Cosine, adj / hyp

$\cos\theta = \dfrac{b}{c}$

Tangent, opp / adj

$\tan\theta = \dfrac{a}{b}$

Unit 1 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items pulled from across all 5 topics. Identifies which misconceptions still bite when you cannot see which topic the question came from.