Displacement, speed, velocity, acceleration and momentum Physics of Motion: Displacement, speed, velocity, acceleration and momentum

We will be considering two kinds of values/quanities… Scalars: Quantities with only a magnitude Examples: Your height, your weight, the distance from the earth to the sun, your instantaneous speed in a car Vectors Quantities with both magnitude and a direction Represented by a point with an arrow emanating from it Length of arrow represents magnitude Direction arrow is pointing represents direction Example: velocity (5 mph north) 5 mph N

What is motion? Change (Δ) in object’s position relative to a reference point

Distance travelled Scalar quantity SI unit: meters (m) Path of object is important in measuring distance travelled

Displacement Vector quantity Length and direction of change in object’s position Consider starting point and ending point, but not HOW it got there

Example: baseball runner A girl hits a baseball while at bat, and runs to first base, then runs 20 feet toward second base, and turns around and runs back to first base, where she is safe. Assuming second base is due north of home plate, what is a) the distance traveled by the runner, and b) the displacement of the runner? (A baseball diamond has sides of 90 feet)

Speed Speed Average speed Scalar quantity Distance traveled per (divided by) period of time s = d/t SI units: m/s Average speed s = d/t, where d is total distance and t is total time. Path of travel must be considered, NOT displacement

Speed Instantaneous speed The speed of an object at any given moment of time For a car, what the speedometer reads May be less than or greater than the average speed at any given time. time

Speed Practice: driving to school Total distance = 3.0 miles Total time = 8.25 minutes What is the average speed in miles per hour (mph)? During what circumstances would the instantaneous speed be: less than the average speed? More than the average speed?

Velocity Vector quantity: magnitude and direction The magnitude of a velocity is a speed v = d/t in a given direction Example: 2 cars, one moving northbound on a highway, the other moving southbound, both with speeds of 25 m/s v1 = 25 m/s north (+ 25 mph) v2 = 25 m/s south (- 25 mph)

Relative motion For objects moving along the same line… Subtract the velocity of the reference point from the velocity of the second object Negative velocities in one direction are equivalent to the same velocity in the opposite direction Think: are the objects moving farther apart or closer together?

Calculating relative velocity B’s velocity relative to A 10 m/s W – 5 m/s W = 5 m/s W 5 m/s W – 10 m/s W = -5 m/s W = 5 m/s E 10 m/s E – (-5 m/s E) = 15 m/s E 10 m/s W – (-5 m/s W) = 15 m/s W Object A Object B 5 m/s West 10 m/s West 10 m/s West 5 m/s West 5 m/s West 10 m/s East 5 m/s East 10 m/s West

Practice problem A family flees Northwest in a car traveling 30.0 mph from a hurricane traveling toward them, northwest at 20.0 mph. How fast is the hurricane moving from the point of view of the family in the car? Assuming the velocities of the hurricane and car do not change, how long will it take for the family put 100 miles between them and the hurricane?

Velocity does not translate to fun Acceleration does!

Acceleration Change in velocity per time 𝑎= ∆𝑣 𝑡 = 𝑣𝑓−𝑣𝑖 𝑡 Vector quantity—direction matters! Two examples: Changing speed Changing direction Positive acceleration means speeding up Negative acceleration means slowing down

Calculating acceleration example Initially, a car is travelling 30. m/s southbound. 5.0 seconds later, it is travelling 15 m/s southbound. What is its acceleration? Has the car sped up or slowed down?

Experiencing a constant speed but changing velocity

Acceleration—changing direction Because velocity is a vector with a direction, changing direction of movement is acceleration Examples: carousel ride or taking a turn at a constant speed Turning at a constant speed, an object’s… Velocity constantly changes. Is therefore accelerating toward the center of the turn (centripetal acceleration) The acceleration is also constantly changing in direction but not magnitude v = 2 m/s E a = 0.4 m/s2 S v = 2 m/s W a = 0.4 m/s2 N

Momentum (p) Related to how difficult it is to stop a moving object or get a resting object to move p = mv Vector quantity Units: kg·m/s The more massive and the faster an object is, the more momentum it has.

Momentum Practice Which has more momentum (magnitude)? A high school football linebacker sprinting at you 10.0 miles per hour, or a rubber band launched at you at 10.0 miles per hour? Which has more momentum? A baseball thrown at 15.0 m/s away from you, or a baseball thrown 30.0 m/s away from you? If the baseball has a mass of 145 grams, what is its momentum if it is thrown 30.0 m/s south?