Methods of Motion Physics I

Some Physics Quantities Vector - quantity with both magnitude (size) and direction Scalar - quantity with magnitude only Vectors: Displacement Velocity Acceleration Momentum Force Scalars: Distance Speed Time Mass Energy

Example: Mass vs. Weight Scalar (no direction) Measures the amount of matter in an object Weight Vector (points toward center of Earth) Force of gravity on an object On the moon, your mass would be the same, but the magnitude of your weight would be less.

Vectors Vectors are represented with arrows The length of the arrow represents the magnitude (how far, how fast, how strong, etc, depending on the type of vector). The arrow points in the directions of the force, motion, displacement, etc. It is often specified by an angle. 5 m/s 42°

Units are not the same as quantities! Quantity . . . Unit (symbol) Displacement & Distance . . . meter (m) Time . . . second (s) Velocity & Speed . . . (m/s) Acceleration . . . (m/s2) Mass . . . kilogram (kg) Momentum . . . (kg · m/s) Force . . .Newton (N) Energy . . . Joule (J)

SI Prefixes Little Guys Big Guys

Kinematics definitions Kinematics – branch of physics; study of motion Position (x) – where you are located Distance (d ) – how far you have traveled, regardless of direction Displacement (x) – where you are in relation to where you started

Distance - How far you travel regardless of direction. Displacement Displacement (x or y)   "Change in position" It is not necessarily the total distance traveled. In fact, displacement and distance are entirely different concepts. Displacement is relative to an axis. "x" displacement means you are moving horizontally either right or left. "y" displacement means you are moving vertically either up or down. The word change is expressed using the Greek letter DELTA (Δ). To find the change you ALWAYS subtract your FINAL - INITIAL position It is therefore expressed as either   Δx = xf - xi or Δy = yf - yi Distance - How far you travel regardless of direction.

Distance vs. Displacement You drive the path, and your odometer goes up by 8 miles (your distance). Your displacement is the shorter directed distance from start to stop (green arrow). What if you drove in a circle? start stop

Example Suppose a person moves in a straight line from the lockers( at a position  x = 1.0 m) toward the physics lab (at a position x = 9.0 m) , as shown below The answer is positive so the person must have been traveling horizontally to the right.

Example Suppose the person turns around! The answer is negative so the person must have been traveling horizontally to the left What is the DISPLACEMENT for the entire trip? What is the total DISTANCE for the entire trip?

Average Velocity 𝑣 = ∆𝑥 ∆𝑡 = 𝑥 𝑓𝑖𝑛𝑎𝑙 − 𝑥 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑡 𝑓𝑖𝑛𝑎𝑙 − 𝑡 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 Velocity is defined as: “The RATE at which DISPLACEMENT changes”. Rate = ANY quantity divided by TIME. 𝑣 = ∆𝑥 ∆𝑡 = 𝑥 𝑓𝑖𝑛𝑎𝑙 − 𝑥 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑡 𝑓𝑖𝑛𝑎𝑙 − 𝑡 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 Average SPEED is simply the “RATE at which DISTANCE changes”.

Speed vs. Velocity Speed is a scalar (how fast something is moving regardless of its direction). Ex: v = 20 mph Speed is the magnitude of velocity. Velocity is a combination of speed and direction. Ex: v = 20 mph at 15 south of west The symbol for speed is v. The symbol for velocity is type written in bold: v or hand written with an arrow: v

Speed vs. Velocity During your 8 mi. trip, which took 15 min., your speedometer displays your instantaneous speed, which varies throughout the trip. Your average speed is 32 mi/hr. Your average velocity is 32 mi/hr in a SE direction. At any point in time, your velocity vector points tangent to your path. The faster you go, the longer your velocity vector.

Average SPEED is simply the “RATE at which DISTANCE changes”. Average Velocity Velocity is defined as: “The RATE at which DISPLACEMENT changes”. Rate = ANY quantity divided by TIME. Average SPEED is simply the “RATE at which DISTANCE changes”.

“m/s” is the derived unit for both speed and velocity. Example A quarterback throws a pass to a defender on the other team who intercepts the football. Assume the defender had to run 50 m away from the quarterback to catch the ball, then 15 m towards the quarterback before he is tackled. The entire play took 8 seconds. Let's look at the defender's average velocity: “m/s” is the derived unit for both speed and velocity. Let's look at the defender's speed:

Average Acceleration Acceleration is the RATE at which VELOCITY changes. A truck accelerates from 10 m/s to 30 m/s in 2.0 seconds. What is the acceleration? Suppose the same truck then slows down to 5 m/s in 4 seconds. What is the acceleration? “m/s/s” or “m/s2” is the derived unit for acceleration.

Acceleration a = -3 = -3 m / s 2 a = +2 mph / s Acceleration – how fast you speed up, slow down, or change direction; it’s the rate at which velocity changes. Two examples: t (s) v (mph) 55 1 57 2 59 3 61 t (s) v (m/s) 34 1 31 2 28 3 25 a = -3 m / s s = -3 m / s 2 a = +2 mph / s

Beware – the signs can confuse! Suppose a ball is thrown straight upwards at 40 m/s. It takes 4 seconds to reach its maximum height, then another 4 seconds back down to the point where it was thrown. Assume it is caught with the same speed it was thrown. Calculate the acceleration upwards and downwards. This negative sign came from using the DELTA This negative sign came from the DIRECTION of the velocity. It is no surprise you get a negative answer both ways as gravity acts DOWNWARDS no matter if the ball goes up or down. It is GRAVITY which changes the ball’s velocity.

What do the “signs”( + or -) mean? Quantity Positive Negative Displacement You are traveling north, east, right, or in the +x or +y direction. You are traveling south, west, left, or in the –x or –y direction. Velocity The rate you are traveling north, east, right, or in the +x or +y direction. The rate you are traveling south, west, left, or in the –x or –y direction. Acceleration Your velocity(speed) is increasing in a positive direction or your speed is decreasing in a negative direction. Your velocity(speed) is decreasing in a positive direction or your speed is increasing in a negative direction.

Velocity & Acceleration Sign Chart + - Moving forward; Speeding up Moving backward; Slowing down Moving forward; Slowing down Moving backward; Speeding up