Distance, Displacement, Speed & Velocity

Distance and Displacement

• Distance measures how far an object has traveled.
• Displacement includes direction, in contrast to distance.
• Distance is a scalar quantity, possessing only magnitude.
• Displacement is a vector quantity, as it has both magnitude and direction.
• If someone walks 8 meters east and then 3 meters west, the total distance traveled is 11 meters, but the displacement is 5 meters (final position minus initial position).
• Displacement can be positive or negative depending on direction, east/north is positive, while west/south is negative.
• 200 miles traveled indicates distance.
• 300 miles north indicates displacement.

Speed

• Speed describes how fast an object is moving.
• A car traveling 30 meters per second covers 30 meters every second.
• Distance = speed x time (d = vt).
• An object moving at a speed of 50 meters per second will take 20 seconds to travel 1000 meters.

Speed vs. Velocity

• Speed is a scalar quantity
• Velocity is a vector quantity
• Speed is always positive
• Velocity can be positive or negative.
• Velocity is speed with direction
• A train moving at 45 meters per second describes speed.
• A train moving at 30 meters per second going west describes velocity.
• Speed tells you how fast something is moving.
• Velocity tells you how fast and where something is moving.
• Average speed = total distance / total time.
• Average velocity = displacement / total time.
• The formula looks the same, but the meaning is different.
• If an object travels 12 meters east and 20 meters west in 4 seconds: average speed is 8 m/s, average velocity is -2 m/s.

Acceleration

• Acceleration is how fast velocity changes.
• A sports car has greater acceleration
• Acceleration = change in velocity / change in time.
• Acceleration = (final velocity - initial velocity) / time.
• If an object starts at 12 m/s and accelerates at 4 m/s², its velocity increases by 4 m/s every second.
• Final velocity = initial velocity + acceleration x time (vf = vi + at).

Speeding Up vs. Slowing Down

• An object speeds up if acceleration and velocity have the same signs.
• An object slows down if they have opposite signs.
• An object moving east at 24 m/s with an acceleration of -6 m/s² is slowing down.

Speed vs. Velocity

• Speed is the absolute value of velocity, must be positive value, indicating how fast an object is moving.
• Velocity includes direction; it can be positive or negative (eastward vs. westward).
• Positive velocity with negative acceleration means slowing down.
• Negative velocity with negative acceleration means speeding up.
• Acceleration and velocity share the same sign, the object speeds up. If they have opposite signs, it slows down.

Gravitational Acceleration

• Represented by 'g', on Earth it's -9.8 meters per second squared and affects vertical velocity.
• Gravitational acceleration varies; the moon's is -1.6 m/s², due to its different mass.
• 'g' acts in the y-direction (vertical), not the x-direction (horizontal).
• Vertical gravitational acceleration (gy or ay) affects Vy, vertical component of velocity; it doesn't affect Vx.

Applying Gravitational Acceleration

• When an object is dropped, its vertical velocity (Vy) becomes increasingly negative due to gravity.
• Each second, the vertical velocity decreases by 9.8 m/s on Earth.
• If a ball is thrown upwards, Vy decreases because the acceleration is negative.
• The ball slows down, reaches max height (Vy = 0), then changes direction and accelerates downwards.

Projectile Motion

• Projectile motion is when an object moves under gravity's influence. Friction is typically ignored.
• One-dimensional projectile motion occurs in the y-direction (up and down).
• Two-dimensional occurs in both x and y directions.

Horizontal and Vertical Velocity Components

• A ball kicked off a cliff has initial horizontal velocity (Vx), then falls downwards.
• Vertical velocity (Vy) changes due to gravity’s constant acceleration.
• Horizontal velocity (Vx) remains constant, unless there's a horizontal force acting on the object.
• Acceleration in the horizontal direction (ax) is zero unless otherwise specified by the problem.

Projectile Motion at an Angle

• Initial velocity (v) at an angle (theta) is resolved into Vx (v * cos(theta)) and Vy (v * sin(theta)).
• Vx remains constant, but Vy changes due to gravity.
• At max height, Vy is zero, but Vx is still constant.
• If the projectile motion is symmetric, Vy has the same magnitude at the same height, but with opposite signs.

Newton's First Law

• An object at rest stays at rest unless acted on by a force.
• An object in motion continues in motion unless acted on by a net force.
• Force is a push or pull action; tension is a force exerted through a rope.
• Friction opposes motion, which slows objects down.
• In space, objects move continuously due to minimal friction.

Newton's Second Law

• Net force (Fnet) equals mass (m) times acceleration (a): F = ma.
• Net force can be in the y or x direction, indicated by summation symbol (sigma).
• A 10 kg mass with 80N force applied accelerates at 8 m/s².
• The velocity of the object increases by 8 m/s every second, related to the applied force.