Unit Two (Motion in Straight Line)
Definition:Motion: is the change in the position of the object with respect to a fixed point as the time
passes
Static Body: - It is a body that does not change its position with time according to a fixed
Point.
Moving (Dynamic) Body: - it is a body changing its position with time according to a fixed
point.
Translational motion: - it is the motion which is characterized by having a starting point and
end point. Ex(motion in a straight line (Train), and projectile motion).
Periodic motion:- it is the motion that repeats itself over equal intervals of time. Ex
(motion in a circle (earth around the sun) and vibrational motion (Pendulum)).
Velocity: it is the displacement moved by the object in one second, or the rate of change of
displacement. It is measured in (m/s) or (km/h), vector, could be positive or negative
according to direction
Speed: - it is the distance moved by the object per unit time, scalar, always positive.
Uniform velocity: - the object velocity when it travelled equal displacements in equal times.
Both the velocity magnitude and direction are constant. (Relation is straight line).
Non uniform velocity: - the object velocity when it travelled unequal displacements in
equal times. Its velocity may change in magnitude or direction. (Relation is Curve not
Straight Line).
Instant velocity: - The velocity of the object at a given instant or point, It can be determined
graphically by the slope of the tangent.
Average velocity: - It is given by dividing the total displacement of the object from the
starting point to the end point by the total time of motion. It can be determined graphically
by the slope of the straight line joining the starting point to the end point.
Acceleration: it is the change of the object velocity per unit time, or the rate of change of
velocity. It is measured in (m/s2) or (km/hr2). Positive acceleration means increasing in the
velocity and negative acceleration (deceleration) means decrease in velocity.
Uniform Acceleration: - the object Acceleration when it changes its velocity with equal
amount in equal times. (Relation is straight line).
Non uniform Acceleration: - the object Acceleration when it changes its velocity with
unequal amount in equal times. (Relation is Curve not Straight Line).
Free Fall acceleration: - it is the uniform acceleration by which objects fall freely towards
Earth’s surface.
Newton’s First Law of motion: - A static object keeps its state of rest, and a moving object
keeps its state of motion at uniform velocity in a straight line unless a resultant force acts
upon it.
Inertia: - it is the resistance of the body to change its static or dynamic state.
Newton’s Second Law of motion: - When a resultant force acts on an object, the object
moves with an acceleration directly proportional to the resultant force and inversely
proportional to the object mass.
Newton: - it is the force that when acts on an object of mass 1 kg accelerates it at 1 m/s2.
Mass: - It is the resistance of the body to change its Kinematic state, Scalar, does not
change.
Weight: - it is the force of gravity acting on the body, vector, change according to the
gravity.
Newton’s Third Law of motion: - For every action there is a reaction equal in magnitude
and opposite in direction.
Graphics
Velocity = Zero
Uniform Velocity (Constant
velocity)
Non uniform velocity
Instantaneous velocity
Deceleration(negative
acceleration)
Uniform acceleration
Avarage veocity
Acceleration = zero
Acceleration(positive
Acceleration)
Non uniform acceleration
Equations
𝑣=
Δ𝑑
Δ𝑡
𝑣𝑎𝑣 =
(Velocity Equation. where v is velocity, d is displacement, t is time).
𝑣𝑓+𝑣𝑖
2
(Average velocity Eq, where vav is average velocity, vf final velocity, vi initial
velocity).
𝑎=
Δ𝑣
Δ𝑡
(a is acceleration, v is velocity, t is time).
Equation of motion in staight line:- three equation
𝑣𝑓 = 𝑣𝑖 + 𝑎 ∗ 𝑡,
𝑎 ∗ 𝑡2
𝑑 = 𝑣𝑖 ∗ 𝑡 +
,
2
2 ∗ 𝑎 ∗ 𝑑 = 𝑣𝑓 2 − 𝑣𝑖 2
Where vf is final velocity, vi is initial or start velocity, a is acceleration, t is time, d is
displacement.
Note:Body start from rest vi = 0, Body stops and the end vf=0, uniform velocity a = 0, moving in
vertical direction a = g.
Equation of motion in parabolic path (Projectile motion)
−𝑣𝑖𝑦
𝑡=
,
𝑔
−2 ∗ 𝑣𝑖𝑦
𝑇 =2∗𝑡 =
,
𝑔
𝑣𝑖𝑦 2
ℎ=
,
2∗𝑔
𝑅 = 𝑣𝑖𝑥 ∗ 𝑇 = 2 ∗ 𝑣𝑥 ∗ 𝑡
Where t is time till max height (half time), T is the flight time or total time, h is max height,
R is the range or horizontal displacement. Viy is the initial velocity component at y
direction; vix is the initial velocity component at x direction.
𝑣𝑖𝑥 = 𝑣𝑖 ∗ cos 𝜃,
𝑣𝑖𝑦 = 𝑣𝑖 ∗ sin 𝜃
Force Equation (Newton's Laws)
∑ 𝐹 = 0 Inertia law or newton's first law.
𝐹 = 𝑚 ∗ 𝑎 Newton's second law. (m is mass, a is acceleration, F is force)
𝐹1 = −𝐹2 Newton's third law (action and reaction law).
𝑤 = 𝑚 ∗ 𝑔 (w is weight, m is mass, g is gravity)
Do not forget vectors opposite the reference (positive direction) is negative