Chapter 3- Linear Kinematics

What is linear kinematics?

The study of describing motion: linear (translation), rectilinear, curvilinear, angular (rotation), or a general combination.

What core questions does kinematics ask?

How far? What direction? How fast? Is the object speeding up or slowing down?

What is position in kinematics?

The location of an object in space, defined at the start, end, or during movement, using a fixed reference point (1D lines, 2D Cartesian coordinates).

What is 2D positioning?

Describing an object’s location in space relative to a frame of reference, usually with respect to the ground (origin).

What is the difference between unlabeled and labeled 3D data?

Unlabeled 3D data shows points of motion, while labeled data uses anatomical landmarks for reference.

What is Visual 3D used for?

To calculate angular kinematics.

How do distance and displacement differ?

Distance is a scalar (path length, magnitude only). Displacement is a vector (difference between start and finish, magnitude and direction).

What formulas represent displacement?

dx = Δx = x final – x initial; dy = Δy = y final – y initial.

What is speed vs. velocity?

Speed is scalar (rate of motion). Velocity is vector (rate of change in position).

Give examples of velocity in sports.

Tennis serve: 125 mph (55.9 m/s); Baseball pitch: 90 mph (40.2 m/s).

How can running velocity be measured?

Marathon: 26.2 mi in 2 hr 10 min (~2.17 hr). Sprint: 100m in 9.79 s. Units: m/s, km/h, ft/s, mph.

What is acceleration?

The rate of change of velocity with respect to time. It is a vector only, no scalar equivalent.

What links position, velocity, and acceleration?

Velocity is the slope of a position curve; acceleration is the slope of a velocity curve.

What happens with positive acceleration in a positive direction?

Velocity increases.

What happens with negative acceleration in a positive direction?

Velocity decreases.

What happens with negative acceleration in a negative direction?

Velocity increases.

What happens with positive acceleration in a negative direction?

Velocity decreases.

What are examples of vertical motion applications?

Jumping, climbing stairs, and elevators.

A sprinter accelerates to 10 m/s in 3 seconds. What is their acceleration?

a = (10 – 0) / 3 = 3.33 m/s².

A baserunner slows from 7 m/s to 0 m/s in 0.5 seconds. What is their acceleration?

a = (0 – 7) / 0.5 = –14 m/s².

What does Newton’s Second Law of Motion state?

Force = mass × acceleration (ΣF = ma).

A weightlifter applies 500 N to a 70 kg barbell over 0.7 seconds. What happens?

Acceleration = 7.14 m/s²; final velocity = 5 m/s.

How does gravity affect objects?

All masses experience g = –9.81 m/s² (–32 ft/s²). Objects going up slow by 9.81 m/s each second; falling objects speed up by 9.81 m/s each second.

What forces influence a projectile’s flight?

Gravity (vertical) and air resistance (both vertical and horizontal, always opposing motion).

What is projectile motion in human movement?

The body or an object can act as a projectile. Performance depends on manipulating or predicting the projectile’s flight.

What equations describe vertical projectile motion?

Equations of uniformly accelerated motion (e.g., vf = vi + gΔt, or vf² = vi² + 2gΔy).

Ja Morant jumps with vi = 4.43 m/s. How long until he reaches peak height?

t = (0 – 4.43) / –9.81 ≈ 0.45 s.

How high does Ja Morant jump with vi = 4.43 m/s?

Δy ≈ 1 m.

What forces affect horizontal projectile motion (if air resistance is negligible)?

None — horizontal acceleration = 0, so horizontal velocity remains constant.

What determines time of flight of a projectile?

Vertical speed and release height. If release and landing heights differ, then t up ≠ t down.

In shot put, if speed = 12 m/s and angle = 30°, what is the horizontal displacement?

Horizontal velocity = 10.4 m/s; total time = 1.22 s; range ≈ 12.7 m.

What three factors influence projectile displacement?

Speed of release, height of release, and angle of release.

What is the theoretical vs. real optimal angle in shot put?

Theory = ~41°; Reality = ~36–37°. Higher angles reduce speed.

What is the theoretical vs. real optimal angle in long jump?

Theory = ~43°; Reality = ~16–24°. Higher angles reduce speed due to longer ground contact.

What are the key summary points of linear kinematics?

Motion types (rectilinear, curvilinear, angular), distance vs. displacement, scalar vs. vector, speed vs. velocity, acceleration, average vs. instantaneous measures, projectile motion, and effects of speed, height, and angle of release.

A ball is thrown at 41° with velocity 10.97 m/s. What are its motion components?

Vertical velocity = 7.2 m/s; Horizontal velocity = 8.28 m/s; max height = 2.64 m; time to peak = 0.734 s; final horizontal velocity = 8.28 m/s.