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Each physical quantity will be either a scalar or a vector.
► Vectors – quantity that must be specified by both magnitude (number and unit) and direction.
Displacement, velocity, force,…
Vectors do not obey the rules of ordinary algebra
► Scalars – quantity that is completely specified by a positive or negative number with appropriate units.
Temperature, length, mass, time, speed, …
Scalars obey the rules of ordinary algebra
► Translational motion – motion along a line through space without rotation.
► Average value – Value over a period of time.
► Instantaneous value – Value at one particular instant/time.
► A frame of reference – is a perspective from which a system (or the universe) is observed together
with a coordinate system used to describe motion of that system.
► Displacement – A change of position in particular direction. A distance in a given direction. Vector. Unit: meter (m)
► Average Velocity – Total displacement divided by total elapsed time
average velocity =
total displacement
⃗ avg
v
total time
x
=
∆t
► Average Speed – Total distance traveled divided by total time.
average speed =
total distance
vavg =
total time
x
t
Average speed = magnitude of average velocity only if motion is 1-D without changing direction;
► (Instantaneous) Velocity – 1. Value of velocity at a particular time.
2. Infinitesimally (vanishingly) small displacement divided by corresponding infinitesimally small time interval.
Direction of velocity is the direction in which the object is moving at that instant.
⃗ =
v
∆x
∆t
as Δt → 0
► (Instantaneous) Speed – 1. Value of speed at a particular time.
2. The magnitude of the instantaneous velocity.
► Acceleration (general) – Time rate of change of velocity.
acceleration =
change in velocity
► Average Acceleration – Total change in velocity divided by time in which that change happened.
► (Instantaneous) Acceleration – The rate of change of velocity over an infinitesimal time interval.
a=
Δv
as Δt  0
Δt
► Acceleration can cause: 1. change in speed (speeding up: v and a in the same direction;
slowing down: v and a in the opposite direction)
2. changing direction
3. both
► Uniform Motion – motion with constant velocity (equal distances in the equal amounts of time)
v avg = v
x = vt
magnitude of velocity = speed
(vector) (m/s2)
time
avg
=
∆v
⃗
∆t
2
► Uniformly Accelerated Motion – motion with constant acceleration a
► Kinematics Equations for 1-D motion with constant acceleration:
u+v
2
𝑎 2
x = ut +
t
2
v = u + vt
x =
vavg =
u+v
t
2
v2 = u2 + 2ax
► Uniform Circular Motion – motion with constant speed around the circular path.
T- period: time needed to one full circle
2 r
r – radius of the circle
speed: v =
T
Average velocity is zero, because displacement for a full circle is zero.
velocity: changing direction - tangent to the path (circle) and constant magnitude (speed)
acceleration – perpendicular to direction of motion, toward the centre and constant magnitude
► Free Fall – is vertical (up and/or down) motion of a body where gravitational force is the only or dominant force acting upon it
Gravitational force gives all bodies regardless of mass or shape, when air resistance can be ignored, the same acceleration.
► Free Fall acceleration – at Earth’s surface is about g = 9.8 m/s2, downward
The speed would decrease by 9.8 m/s every second on the way up, at the top it would
reach zero, and increase by 9.8 m/s for each successive second on the way down
► Free Fall formulas – Formulas are the ones for uniform accelerated motion with a = g
v = u + vt
vavg =
u+v
2
y =
u+v
t
2
y = ut +
g 2
t
2
v2 = u2 + 2gy
remember that in the coordinate system in which upward is chosen to be positive, g is negative.
► Terminal speed/velocity – is maximum velocity an object can reach in air/any fluid.
Air resistance depends on velocity. The greater velocity, greater air resistance, smaller acceleration.
Acceleration is getting smaller due to air resistance and eventually becomes zero when the force of the air resistance equals gravity, the
downward force of gravity is equal to the upward force of air resistance resulting in a zero net force, hence zero acceleration. The
object will stop accelerating and maintain the same speed.
Terminal velocity/speed is different for different bodies.
► Graphs of the motion of an object in
the gravitational field (downward is positive)
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GEOMETRICAL INERPRETATION / GRAPHS OF 1 – D MOTION
► Average Velocity
► ( Instantaneous) Velocity at a given time/point
v avg
Δx
=
t
☻ slope of the straight line joining the
initial and final position on the position-time graph.
v=
Δx
as Δt  0
Δt
☻slope of the tangent line at that point
on the position – time graph.
► (Instantaneous) speed – slope of the line tangent to the distance – time curve at a given point.
► Average Acceleration
► Instantaneous Acceleration at a given time/point
aavg =
Δv
t
☻ slope of the straight line joining the initial and
final position on the velocity – time graph.
► Displacement between two positions/times
☻ displacement is the area under velocity – time graph
between two times/positions
a=
Δv
as Δt  0
Δt
☻ slope of the line tangent to the v vs. t
curve at a time t
► Average velocity between two positions/times
☻ change in velocity Δv is the area under acceleration – time graph
between two times/positions