SPH3U1 - Physics Unit 1

Kinesmatics

The study of motion/how objects move

Scaler Quantities

A quantity that has only magnitude (size)

Ex: Distance

Vector Quantities

A quantity that has both magnitude and direction

Ex: Velocity - Measures speed and direction

Reference point

A place or object used for comparison to determine if something is in motion

Position

The distance and direction of an object from the reference point

Displacemnet

Change in position of an object

Formula:

Total displacement if an object moves more than once

_Formula:

Vector Scale Diagram

Vectors associated with total displacements drawn to a proportionate scale.

Ex:

Directed line Segment

A straight line between 2 points with a specific direction

Difference between speed and velocity

Speed - Deals with how fast an object moves

Velocity - Deals with how fast and what direction an object moves

Average Speed

V_av = Avg Speed

Δd = Total distance

Δt = Total time

Average Velocity

V_av = Avg Velocity

Δd = Total distance + direction

Δt = Total Time

Motion with uniform/constant velocity

Object travels in a straight line with a constant velocity

Motion with non-uniform/constant velocity

Motion in which the object’s speed changes or the object does not travel in a straight line

Ex: Traveling at a constant velocity, but in multiple directions

What is acceleration

Rate of change of velocity (m/s²)

Position-Time Graph: Horizontal Line ABOVE X-Axis

• No velocity - object at rest 

• Slope = 0

• Stationed east of the reference point

Velocity and Acceleration Time Graphs if position-time graph is a horizontal line ABOVE x-axis

Position-Time Graph: Horizontal Line BELOW X-Axis

• No velocity - object at rest

• Slope = 0

• Stationed WEST of reference point

Velocity and Acceleration Time Graphs if position-time graph is a horizontal line BELOW x-axis

Position-Time Graph: Gradual Positive Slope

• Straight Line =  Constant Velocity

• Positive Slope = Displacement in y-axis indicator

• Y-axis title indicates direction

Velocity and Acceleration Time Graphs if position-time graph is a gradual positive slope

Position-Time Graph: Steep Positive Slope

• Straight Line =  Constant Velocity

• Positive Slope = Displacement in y-axis indicator

• Y-axis title indicates direction

Velocity and Acceleration Time Graphs if position-time graph is a STEEP positive slope

Position-Time Graph: Negative Slope

• Straight line = Constant Velocity

• Negative Slope = Displacement in a negative Eastward direction until it passes the reference point.

• If slope passes the x-axis or reference point object starts moving in the opposite direction

Velocity and Acceleration Time Graphs if position-time graph is a negative slope

Position-Time Graph: Positive Parabola ABOVE the horizontal line

• Object speeding up EASTWARD

• Upward parabola above X-Axis = Object speeding up

Velocity and Acceleration Time Graphs if position-time graph is a Positive Parabola ABOVE the horizontal line

Position-Time Graph: Positive Parabola BELOW the horizontal line

• Object slowing down WESTWARD

• Negative velocity

Velocity and Acceleration Time Graphs if position-time graph is a Positive Parabola BELOW the horizontal line

Position-Time Graph: Negative Parabola ABOVE the horizontal line

Object slowing down EASTWARD

Velocity and Acceleration Time Graphs if position-time graph is a Negative Parabola ABOVE the horizontal line

Position-Time Graph: Negative Parabola BELOW the horizontal line

Object speeding up WESTWARD - moving in a negative direction

Velocity and Acceleration Time Graphs if position-time graph is a Negative Parabola BELOW the horizontal line

How to go from time graph to time graph

Position —> Velocity —> Acceleration

• Find the SLOPE

Acceleration —> Velocity —> Position

• Find the AREA

Instantaneous Velocity

Velocity at a specific interval of time

• Ex: A car is moving for 10 seconds, and you must find the instantaneous velocity from 6-7 seconds

Equation 1

Variables Found: Δd, Δt, V_f, V_I

Variables Not Found: a_av

Equation 2

Variables Found: Δt, V_f, V_I, a_av

Variables Not Found: Δd

Equation 3

Variables Found: Δd, Δt, V_I, a_av

Variables Not Found: V_f

• When trying to find Δt it can be tricky if initial velocity is not 0 

• However, using quadratic equations (ax²+bx+c) it can be solved by rearranging the formula and using the quadratic formula to find the roots.

Equation 4

Variables Found: Δd, V_f, V_I, a_av

Variables Not Found: Δt

Equation 5

Variables Found: Δd, Δt, V_f, a_av

Variables Not Found: V_I

What is the value of g

g = 9.8m/s²

Object’s acceleration if moving up or down

• If the object is moving down, the g = -9.8m/s²

• If the object is moving up, the g = 9.8m/s²

Positive and Negative Convention

• If the object is moving left and down then it is going to be NEGATIVE (-)

• If the object is moving right or up then it is going to be POSITIVE (+)

Steps in solving problems involving gravitational pull:

Question: A flowerpot is knocked off a window ledge and accelerates uniformly to the ground. If the window ledge is 10.0 m above the ground and there is no air resistance, how long does it take the flowerpot to reach the ground?

• Using equation 3: find the variables that have been given

  • In this case:

  • Required: Time

• Rearrange the formula to isolate the variable →

  • V_iΔt is canceled out due to initial velocity being 0

• Lastly, plug in the numbers