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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