Motion: One-Dimensional Kinematics

Flashcards covering position, displacement, velocity, speed, acceleration, and the key kinematic equations, including simple example calculations and graph concepts.

What are the three main types of motion?

Translational (linear), rotational (circular), and vibrational (e.g., pendulum).

In the particle model of motion, what is a 'particle'?

A point-like object with mass but infinitesimal size.

How is position defined in one dimension?

The location of a particle with respect to a chosen reference point (origin); it can be positive or negative along the axis.

What is displacement ∆x?

The change in position: ∆x = x2 − x1; a vector with magnitude and direction.

If a particle moves from x1 = 5 m to x2 = 12 m, what is ∆x?

∆x = +7 m (positive direction).

If a particle moves from x1 = 5 m to x2 = 1 m, what is ∆x?

∆x = −4 m (negative direction).

What does the magnitude of displacement represent?

The distance from the origin to the final position; the sign indicates direction; displacement is a vector.

What is average velocity?

v_avg = ∆x/∆t = (x2 − x1)/(t2 − t1); it is a vector quantity with magnitude and direction.

What is average speed?

s = total distance traveled / total time; a scalar quantity.

Compute the average velocity for xA = 30 m at tA = 30 s and xB = −53 m at tB = 50 s.

vavg = (xB − xA)/(tB − t_A) = (−53 − 30)/(50 − 30) = −83/20 = −4.15 m/s.

What is instantaneous velocity?

The velocity at a specific time: v = dx/dt = lim Δt→0 Δx/Δt; the rate at which position changes at that instant.

How is instantaneous velocity represented on a displacement–time graph?

As the slope of the x–t curve at that instant.

What is acceleration?

The rate of change of velocity: instantaneous a = dv/dt = d^2x/dt^2.

How is average acceleration defined?

a_avg = Δv/Δt = (v2 − v1)/(t2 − t1).

On a velocity-time graph, what does a straight line indicate about acceleration?

Constant (uniform) acceleration; the slope of the v–t graph equals the acceleration.

What is the equation for velocity with constant acceleration?

v = v0 + a t.

What is the equation for displacement with constant acceleration?

x = x0 + v0 t + 1/2 a t^2.

What is the relation that links final velocity, initial velocity, acceleration, and displacement without time?

v^2 = v0^2 + 2 a (x − x0).

If x(t) = 4 − 27t − t^2, what is the velocity at t = 2 s?

v = dx/dt = −27 − 2t; at t = 2, v = −31 m/s.

For x(t) = 12 t^2 − 2 t^3, find v and a at t = 3 s.

v = dx/dt = 24t − 6t^2; at t = 3, v = 18 m/s. a = dv/dt = 24 − 12t; at t = 3, a = −12 m/s^2.