CHAPTER THREEMOTION IN STRAIGHT LINEMotion:It is changing
position of the body in space with timeTypes of motion:1- Periodic
motion: The motion which has no initial or final point and repeats
itself periodicallyEx: motion in a circle vibration motion wave
motion 2- Transition motion: The motion which has initial and final
pointEx: Motion in straight line projectiles bus, cars .....
etcSpeedVelocity
Scalar Vector
Covered distance in one secondCovered displacement in one
second
Always positiveAlways negative
The law: The law:
Types of velocity:Uniform velocity(constant)Variable
velocityInstantaneous velocityAverage velocity
The body cover equal displacement in equal times in straight
lineThe body cover different displacement in different timesThe
velocity of the body at a certain momentTotal displacement divided
by total time
Straight line curve find slope at the V av =(d / t) total
Required moment = slope of total lineAverage speed = Average
velocity = Examples:1- A person drives a car he covered 8.4 km in
0.12 h then he is out of fuel, he left the car and walked to fuel
station 2 km away in 0.5 h. Find average velocity numerically and
graphically. 2- In the previous problem the person returned back in
0.6 h to his car find the average speed and average
velocity.Note:To convert velocity from unit km/hr into m/s x For
example: 180 km/hr = 180 x 5/18 = 50 m/sAcceleration It is the
change of velocity in one second It is the rate of change in
velocity (rate = in one second and, divide by time)a = Example:
from the table find acceleration
Types of acceleration:1- Positive (when velocity increases) 2-
Negative (when velocity decreases) its named deceleration3- Zero
(when velocity is constant) slope = a = Chapter four Equations of
motionG.R: When a body moves with uniform velocity the acceleration
= zero?Because, a= and vf = vi so, a=0We will start from these two
equation keysa= V av = Prove 1st equation of motion?at = Vf Viat +
Vi=Vf
Prove 2nd equation of motion?
Prove 3rd equation of motion?
Prove 2nd equation of motion graphically?
Distance travelled = area under the line =area of rectangle +
area of triangle= vi t + (vf -vi)t
But acceleration = (vf -vi)t and so (vf -vi) = at therefore:
Distance travelled (d) = vi t + (vf -vi) t = vi t + [at]t = vi t
+ at2d = vi t + at2
Example problems:1-An airplane accelerates down a runway at 3.20
m/s2for 32.8 s until is finally lifts off the ground. Determine the
distance travelled before takeoff.2-A car starts from rest and
accelerates uniformly over a time of 5.21 seconds for a distance of
110 m. Determine the acceleration of the car.3-A race car
accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds.
Determine the distance travelled.4-A bike accelerates uniformly
from rest to a speed of 7.10 m/s over a distance of 35.4 m.
Determine the acceleration of the bike.5-A plane has a takeoff
speed of 88.3 m/s and requires 1365 m to reach that speed.
Determine the acceleration of the plane and the time required to
reach this speed.6. A car travelling at 20 ms-1accelerates steadily
at 5 ms-2for a distance of 70 m. What is the final velocity of the
car?7- A person drives a car with constant speed 30 m/s, suddenly a
boy rushed across the street, the time of reaction to press brakes
was 0.5 second, then the car decelerate by 9 m/s2 till it stopped.
Find the total covered distance? The free fall acceleration or
acceleration due to gravity (g):When a body falls free, its
velocity increases each second by 9.8 m/s as shown in the
figure:
*The body has acceleration called free fall acceleration or
acceleration due to gravity g* Sometimes g is taken to equal 10
m/s2 as in the figure:
All bodies have the same acceleration, but heavy bodies reach
earth first because the air resistance on them is very small while
it is very large on light bodies, if air resistance is neglected so
all bodies reach earth in same time as in the figure:
*The three equations of motion are applied here, just remove a
and put instead gProblems:1- A body falls from deck of a skyscraper
370 m above the street. Determine the time required for the body to
free fall from the deck to the street below.2- A stone is dropped
into a deep well and is heard to hit the water 3.41 s after being
dropped. Determine the depth of the well.3- How long does it take a
ball to reach the ground 7.0 m below, if it is thrown straight up
with an initial speed of 2.00 m/s?4-A ball is thrown straight up
with a speed of 4.6 m/s. How long does the ball take to reach its
maximum height?5-(For higher students only) An archer shoots an
arrow with an initial velocity of 21 m/s straight up from his bow.
He quickly reloads and shoots another arrow in the same way 3.0 s
later. At what time and height do the arrows meet?6- A stoned falls
from top of a building, it passed a person in a window 5m height
after 4 second. Find:1-Height of building 2- velocity of stone in
front of the person 3- time to touch ground7- An apple fall from a
tree, touch ground after 1 second, find:1- Length of tree 2-
Average speed of falling 3- Velocity of the apple just before touch
ground
Projectiles:A) Vertical upward in straight line:1- When a body
is projected upward, it leaves the hand with initial velocity vi 2-
As the body moves up the velocity decreases (g= - 10 m/s2) till it
stops at max, height3- The body reverse its direction and moves
down with positive acceleration g = 10 m/s2The velocity at any
point during ascending = - velocity at same point during
descending4- Time of ascending = time of descending
The graphs:
Example:From the next table:
Draw the graphs (d-t) and (v-t) From both graphs find velocity
at the points J, A and K Whats the value of the slope in the graph
(v-t) and what does it represent
Projectiles with angle with horizontal X axis:When a ball is
thrown or tank missile or a bow it takes a curved path called
parabola
1- Velocity can be analysed into two components Vx and Vy2- The
horizontal velocity V x is constant all the time and equal V ix =
vi cos (a x = 0)
3- The vertical velocity V y decrease all the time till = 0 at
maximum height V iy = vi sin (a y = g = -10 m/s2) {this is initial
velocity in y direction}
5- At any moment velocity is given from the relation:
6- Time to reach maximum height t : put V y = 0
7- Time of flight:
8- The max, height reached: in 3rd equation put v f y = 0
so,
9- The maximum horizontal range R:Time of max, range = time of
flight T, substitute in 2nd equation (d=R, a=0, t=T)
Examples1-A motorbike launched with velocity 15 m/s and with
angle 30 with horizontal. Find:1- Maximum height reached2- Time of
flight3- Maximum horizontal covered distance (range)Solution:
Question2:A body is projected with a velocity of 20 ms-1at 50oto
the horizontal. Find(i) Maximum height reached(ii) Time of flight
and(iii) Range of the projectile.
Question3:John is on top of the building and jack is down. If
john throws a ball at an angle of 60oand with initial velocity 20
m/s. At what height will the ball reach after 2 s?Solution:Given:
Vyo= 20 m/s, t = 2s,The Vertical velocity in y direction is given
by Vy= Vyosin 60o = 2032 = 17.32 m/s.Vertical distance, y = Vyot
-12gt2 = 202 - 0.59.84 = 20.4 m.
The highest barrier that a projectile can clear is 14 m, when
the projectile is launched at an angle of 30.0 degrees above the
horizontal. What is the projectile's launch speed?Solution:The
maximum height of the projectile is given by the equation:
whereis the launch angle. Then we can find initial velocity:
Graphs: What does this graph represent?The answer is that: 1-Any
graph represent its slope so, we should learn how to find the slope
Slope = ( ( / ( ) 2- Then we look to the shape of the drawn
graphUniform Non-uniform
-Ve uniform= zero
Examples:
Question: draw three graphs represent free fall
acceleration.
Chapter fiveNewtons laws of motionForce is the main reason of
accelerationForce is measured by spiral balanceNewtons 1st law of
motion:The body keeps its state of rest or motion in straight line
with uniform velocity unless affected by a force that changes its
stateMathematical formula: F = 0 Explains:
2- G.R:When you shoot a ball it moves then stops after a
while?Due to friction force3- When F = 0 so, a = 0 so, no change in
velocity and the body keeps moving with same velocity4- To stop a
moving body or to move a rest body that means changing its velocity
(giving acceleration) that requires a forceInertia:It is the
tendency of a rest body to keep rest or the tendency of a moving
body to keep its velocity OR resistance of body to change its
stateExamples on inertia:1- When a bicycle rider hit a stone, he
pushes forward?1st state: motion 2nd state: restDue to inertia the
rider try to keep 1st state so, pushes forward2- When a car
suddenly moves, you push backward?3- When a car suddenly stops, you
push forward?Answer yourself4- You must wear safety belt? 1st
state: motion 2nd state: restDue to inertia the rider try to keep
1st state so, pushes forward but safety belt prevent this deadly
pushing5- Spaceship needs no fuel while travelling in
space?Because, inertia keeps its motion with uniform velocity in
straight line and no resisting force in space Newtons 2nd law of
motion:When a force acts on a body, the gained acceleration is
directly proportional with the force and inversely proportional
with the mass of the bodya f a or F = m . a unit of F = kg.m/s2 = N
, D.F = M L T-2 Newton:It is the force which acts on body of mass 1
kg, gives it acceleration 1 m/s2The graph:
Mass and weight:Mass: it is the resistance of the body to change
its state.Weight: it is the gravity force acts on the body (its
direction: downward towards earth centre)(Weight w = m . g)Newtons
3rd law of motion:
For every action, there is a reaction equal in magnitude but
opposite in directionMathematical formula: F 1 = - F 2
The rocket idea depends on Newton 3rd law where huge amount of
burnt gases push downward so, the reaction of the rocket is to push
upwardNotes:1- There is no single force in universe, the action and
reaction generate together and vanish together2- Action and
reaction are from same type, if action is gravity force so,
reaction is gravity force3- Action and reaction dont cause
equilibrium ( F 0) because, they act on two different
bodiesExample:In the figure: if the mass of elephant is six times
mass of the man and if man moves with a = 2m/s2 find mass of the
elephant (why it is ve) and why there is no equilibrium?
Mass mWeight wt
The amount of matter contained in a bodyThe gravity force acts
on the body
M = wt / gWt = m g
Constant (At moon and earth it is equal)Variable (Weight on moon
= 1/6 weight on earth)
ScalarVector
FundamentalDerived
Unit: KgUnit: Newton
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