SPH3U [Unit 1: Kinematics]
Lesson 1 : [MOTION INTRODUCTION]
Mechanics: The study of motion. Mechanics consist of KINEMATICS and DYNAMICS.
Kinematics: The description of motion.
Kinematics Terminology
Scalar quantities: A measured quantity with a magnitude and units.
EG:________________
Vector quantities: A measured quantity with a magnitude, units, and direction. EG:_________________
Distance (Δd): the amount of space between two objects or points, measured in millimetres (mm),
centimetres (cm), metres (m) or kilometres (km).
⃑ ): The straight line distance and direction from a reference point.
Position (𝒅
⃑ ): The change in an object’s position. The displacement only requires knowledge of
Displacement (∆𝒅
⃑ 𝟏 ) and final position (𝒅
⃑ 𝟐 ) of an object.
the initial position (𝒅
Time (Δt): the duration measured in seconds (s), minutes (min) or hours (h).
Speed (v): how quickly an object is moving, measured in km/h or m/s.
Instantaneous speed (vinst): the speed at which an object is travelling at a particular instant
Average Speed (vav): the total distance divided by the total time for a trip, measured in m/s or km/h.
Rate of change of distance.
⃑ ): the total displacement divided by the total time for a trip, measured in m/s or
Average velocity (𝒗
km/h. Rate of change of position.
Note: Δ is the Greek letter delta, and means “the change in”. For example, Δt means “the change in
time”.
Formula for Average Speed:
vav = Δd
Δt
Δd = d2 – d1
d1 – initial distance (often it is zero)
d2 – final distance
Δt = t2 – t1
t1 – initial time
t2 – final time
SPH3U [Unit 1: Kinematics]
Lesson 1 : [MOTION INTRODUCTION]
Example 1:
Lucy took the bus from her house to Burlington Mall. It took her 0.50 h to get there, and the mall is 6.5
km from her house. What was her average speed?
Formula if positions are given:
∆𝑑 = ⃑⃑⃑⃑
𝑑𝑓 − ⃑⃑⃑
𝑑𝑖
⃑⃑⃑
𝑑𝑖 = initial position
⃑⃑⃑⃑
𝑑𝑓 = final position
* position vectors are measured with respect to the origin of a co-ordinate system used to
measure displacement.
Example 2: A car is 325 m [W] of a stop sign. It changes position to 425 [E] of the stop sign. What is the
car’s displacement?
⃑⃑⃑𝑖 =
Known: 𝑑
425 [E] = ____ [W]
⃑⃑⃑⃑
𝑑𝑓 =
Unknown: ∆𝑑 =
Formula if displacements are given:
∆𝑑 = ∆𝑑1 + ∆𝑑2
∆𝑑1 = displacement 1
∆𝑑2 = displacement 2
*displacement vectors represent how far an object has travelled.
SPH3U [Unit 1: Kinematics]
Lesson 1 : [MOTION INTRODUCTION]
Example 3: A car drives 75.6 m forward along the road, then reverses for 15.2 m. What is the car’s total
displacement?
Known:
Unknown:
Example 4: Jog 100 m north, then 200 m east, then 100 m south. If this takes 200 seconds:
a)
What distance is travelled?
b)
What is the final displacement?