Vectors and Scalars

• Vectors and scalars differentiate physical quantities based on whether direction is needed to describe them fully.

Vector vs. Scalar

• A vector is a quantity with both magnitude (size) and direction.
• A scalar is a quantity with only magnitude.

Scalar or Vector Examples

• Jimmy ran 5m East (vector).
• Brenda placed her pencil 3 inches from her binder (scalar).
• The car had an acceleration of 5m/s² North (vector).
• The ant walked at a velocity of -3mm/s (vector).
• Displacement (vector).
• Velocity (vector).
• Distance (scalar).
• Acceleration (vector).
• Speed (scalar).
• Time (scalar).

Defining Key Terms

• Distance refers to how much ground an object has covered during its motion.
• Displacement refers to the change in position of an object.
• Speed is how fast an object is moving, regardless of direction.
• Velocity is the rate at which an object changes its position, including direction.
• Acceleration is the rate at which an object's velocity changes over time.

Number Line Displacement

• To find the displacement using a number line, determine the final position relative to the starting position (origin).
• The objects' positions from the origin are: Car C = -5 miles, Car A = +5 miles, Car B = -10 miles, School = +10 miles.
• For a car with an initial position of +5 and a final position of -9, the displacement Δx = -9 - (+5) = -14.

Calculations

• For a water balloon thrown upwards, the time interval for the balloon to fall from its peak to Chantal is 3.13 s - 1.43 s = 1.7 s.
• For a car traveling 75 km [south] in 0.75 hours, the velocity is 75 km / 0.75 h = 100 km/h [south].
• To find how many seconds it will take for a motorboat traveling 40.0 km/h to cross a 2.0 km wide lake: Convert speed to km/s: 40.0 km/h ÷ 3600 s/h = 0.0111 km/s, Solve for time: 2.0 km ÷ 0.0111 km/s = 180.18 seconds.

Marathon Training

• Yuan runs 22 km [N], then 32 km [S] in 4.2 hours.
• Yuan's displacement at the end of the run is 32 km - 22 km = 10 km [S].
• The total distance Yuan traveled is 22 km + 32 km = 54 km.
• Yuan's average speed is 54 km / 4.2 h = 12.86 km/h.
• Yuan's average velocity is 10 km [S] / 4.2 h = 2.38 km/h [S].

Triathlon Training

• Elliot swims 2 km [N], bikes 25 km [W], then runs 2 km [S] in 2.3 hours.
• The total distance Elliot traveled is 2 km + 25 km + 2 km = 29 km.

Car Acceleration

• Katherine accelerates from 5.0 m/s [E] to 15.0 m/s [E] in 2.0 s.
• The change in velocity is 15.0 m/s - 5.0 m/s = 10.0 m/s [E].
• The acceleration is (10.0 m/s) / 2.0 s = 5.0 m/s² [E].

Approaching a Stoplight

• Zach is moving at +30.0 m/s and decelerates at -8.00 m/s² until stopping.
• The change in velocity is -30.0 m/s.
• The time it takes Zach to stop is (30.0 m/s) / (8.00 m/s²) = 3.75 s.
• Negative acceleration means the acceleration is in the opposite direction to the velocity, causing the object to slow down.

Canoe Travel Distance

• To find how far a canoe travels at 8.0 km/h for 33 seconds, convert seconds to hours: 33 s / 3600 s/h = 0.009167 h.
• Distance = 8.0 km/h * 0.009167 h = 0.0733 km.

Airplane Speed

• An airplane travels 2310 km in 2.5 hours.
• The speed in km/h is 2310 km / 2.5 h = 924 km/h.
• To convert to m/s, multiply by 1000 to convert km to m, and divide by 3600 to convert hours to seconds: (924 km/h * 1000 m/km) / 3600 s/h = 256.67 m/s.

Athlete Acceleration

• An athlete accelerates at 1.8 m/s² for 3.6 seconds.
• The change in velocity is 1.8 m/s² * 3.6 s = 6.48 m/s.
• If the initial velocity was 1.2 m/s, the final velocity is 1.2 m/s + 6.48 m/s = 7.68 m/s.

Time, Displacement, Velocity, and Acceleration

• If velocity increases and displacement stays the same, the time interval decreases.
• If velocity decreases and the time interval stays the same, the displacement decreases.
• A person walking at a constant velocity decides to walk a longer route, this means their time interval will be longer because they have increased displacement.

Dirtbike Racing

• A dirtbike races around a 6 km track and takes 10 seconds longer on the first round
• The dirtbiker will be travelling faster on the second round.

Cat Acceleration

• A cat accelerates at a rate of +2 m/s². Its starting speed is 5 m/s. After 3 seconds, it will be going 11 m/s.

Newton's First Law

• Newton's first law states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a force.
• Newton's first law is often called the law of inertia.
• Inertia is the tendency of an object to resist changes in its state of motion.
• A bowling ball has more inertia than a golf ball due to its greater mass.
• Passengers in a car lurch forward when it suddenly stops because of inertia. A seatbelt helps by providing a force to stop the passenger's forward motion.

Newton's Second Law

• Newton's second law states that the acceleration of an object is directly proportional to the net force acting on the object, is in the same direction as the net force, and is inversely proportional to the mass of the object.
• Equation: F = ma (Force = mass x acceleration).
• If the force is tripled on an object, the acceleration will triple, assuming mass remains constant.
• If the mass of an object is doubled and the force remains constant, the acceleration will be halved.
• For an object with a mass of 150kg accelerating at 1.5 m/s², the force acting on the object is F = 150 kg * 1.5 m/s² = 225 N.
• An object undergoing a force of 15N with a mass of 6.7kg will accelerate at a = 15 N / 6.7 kg = 2.24 m/s².
• For an object slowing down at a rate of 0.35m/s² due to a force of 7N, the mass of the object is m = 7 N / 0.35 m/s² = 20 kg.

Newton's Third Law

• Newton's third law states that for every action, there is an equal and opposite reaction. If someone pushes against a wall with 20N of force and it doesn't move, the wall is pushing back with an equal force of 20N in the opposite direction.
• Hitting a baseball with a bat the action is the bat hitting the ball, the reaction is the ball pushing back on the bat. The ball will fly off.
• Bowling ball knocking down some bowling pins the action is the ball hitting the pins, the reaction is the pins pushing back on the ball. The pins will fall over.
• A fish swimming forward in the water the action is the fish pushing water backward, the reaction is the water pushing the fish forward. The fish moves forward.

Pressure

• The factors that affect pressure are force and area.
• In physics, pressure is defined as the force over a given area.
• The standard unit of measure for pressure is Pascal (Pa).
• On a cold winter day, a basketball feels deflated because the air molecules inside the ball have less kinetic energy, resulting in lower pressure and volume.

Pressure Cont...

• The pressure inside a sealed car tire might increase on a hot summer day because the heat increases the kinetic energy of the air molecules, leading to higher pressure.
• Air pressure is lower on top of a mountain compared to the beach.
• With a 40 N block exerting 20 Pa of pressure, the area of the block touching the table is A = 40 N / 20 Pa = 2 m².
• A 10 N box with equal sides of 1 meter will exert a pressure of P = 10 N / (1 m * 1 m) = 10 Pa.
• Water pressure increases the deeper you are because there is more water above, exerting greater force due to its weight.
• A sharp knife would exert more pressure than a dull knife because it concentrates the force over a smaller area, allowing it to cut more easily.