__Specific objectives.__

- Define motion.
- Find linear quantities i.e. distance, displacement, speed, velocity and acceleration.
- Describe experiment to determine velocity and acceleration.
- Plot and explain motion graphs.
- Apply the equation of uniform accelerated motion to solve numerical problems.
- Determine acceleration due to gravity.

__Motion.__

- Is the act of changing position.

__Types of motion.__

__Translational motion.__

- Is the motion or movement from one position to another either through a straight line called linear motion or path called non- linearmotion.

__Rotational motion. __

- Is the movement or spinning round an axis e.g. rotation of the earth.

__Oscillatory motion.__

- Is the vibration to and from along a path.

__Translational motion.__

__Linear motion.__- Is the motion along a straight line in a specific direction.
- There are quantities considered in this motion called linear quantities and these are;

**Distance.**

- Is the length of a path covered by a body in a given time.
- It is measured along the actual path taken by the moving body.
- It is measured in meters.
- It is a scalar quantity.

**Displacement.**

- The length between initial position and final position in a specific direction.
- It is measured in meters and it is a vector quantity.

**Speed.**

- The total distance covered in a unit time.

S = distance covered/time taken

SI units = m/s

- It is a scalar quantity.

**Velocity.**

- Is the rate of change of position in a certain direction.
- It is displacement per unit time.

V = displacement/time

SI unite = m/s

- It is a vector quantity.

__Uniform or constant velocity.__

- It is when a body covers equal displacement at equal time interval no matter how small the time interval is.
- The velocity at a particular time is called instantaneous velocity.

__Non- uniform velocity.__

- Is when a body covers different displacements at equal time travel.
- The displacement is given by

Displacement = average velocity + time

**Acceleration.**

- The rate of change of velocity.

A = (final velocity – initial velocity) /time taken

SI units = m/s²

- It is a vector quantity.

__Zero acceleration.__

- This is when the velocity does not change.
- It is when a body is moving with uniform velocity.

__Negative acceleration or deceleration or retardation.__

- It is when a body slows down.
- It is when the velocity is decreasing with time.

__Positive acceleration.__

- When the velocity is increasing with time.

__Uniform acceleration.__

- When the velocity changes regularly with time, that is when the velocity changes by equal amount in equal time travel no matter how small the time interval may be.

__Equation of linear motion. (Uniform motion)__

- Consider a body and mass moving with a velocity U. A force act on the body and after time T, the body attains velocity V after covering a distance S.

- The acceleration is represented by

a = change of velocity/time

a = (V – U) /T

at = V – U

V = at + U T = (V – U)/a

- The displacement S of the body.

S = average velocity x time.

S = Ut + ½ at^{2}

- The displacement S = average velocity x time

2aS = V^{2} – U^{2}

V^{2} = U^{2} + 2aS

__Measurement of velocity, speed and acceleration.__

__Speed/velocity.____Using a tape measure.__

- The sped of a body can be measured using a tape measure or a rule and a stop watch.
- Measure the length of a given distance or path e.g. field in meters.
- Let one run round the field once and record the time taken.
- Calculate the average speed from the equation.

Average speed = total displacement covered/total time

= perimeter/time

Velocity.

- Measure the distance in straight line in a given direction e.g. 100m strip.
- Measure the time taken to run the strip.

Velocity = displacement/time

__Using a ticker timer.__

- Ticker timer is a device that vibrates regularly due to charging current in the main supply.
- It works on the principal of magnetic effect of electric current.
- Has an arm which vibrates regularly and makes dots on a moving paper tape.
- Successive dots are marked on the same interval of time.
- It operates at a frequency of 50Hz i.e. it makes 50 dots in every second.
- The time interval between two consecutive dots is 1/50 = 0.02 seconds. It is called a tick.
- The distance between two successful dots is the distance covered by the tape in 0.02 seconds.
- It is usually measured in ten- tick since it is very small. Time for 10 ticks = 10 x 0.02 = 0.2 seconds

__EXP: TO DETERMINE THE VELOCITY OF A TROLLEY USING A TICKER TIMER.__

__Requirements.__

- AC power source.
- Ticker timer.
- Tape.

__Procedure.__

- Set up the run way such that when the trolley is given a small push it runs down with constant velocity.
- Using an inclined plane, let the trolley move down the runway pulling the tape.
- Ignoring the first few dots, cut a tape with 10 dots i.e. ten- tick.
- Measure the length and calculate the velocity. Let us assume that the distance covered was 7.6 meters.

__Solution__

I second = 50Hz

10Hz =0.2 seconds

D =7.6 cm

T = 0.2 seconds

V = = = 38m/s

__Possible motion.__

- Dots spread and are not equally spaced the body is moving with changing velocity.
- When the dots are equally spaced, the body is moving with uniform or constant velocity.
- When the dots are close together or get closer and closer, the body is slowing down or its decelerating.

__Motion under gravity.__

- All objects moving or falling under the influence of gravitational force have a constant acceleration.
- The time taken by a falling body to reach the surface of the earth will be determined by the distance of the fall but not the mass of the body.
- If the effect of air resistance is ignored, all bodies, light or heavy, when dropped from the same place, fall down through the same height in the same time and that their final velocity is the same.
- A stone and a feather will drop together in vacuum at the same time, however, a stone and a sheet of paper released together at a given height above the ground in space do not reach the ground together
- This is because the air resistance has much deterring effect on large surface area on the negatively light paper.
- As the body falls, they accelerate uniformly. This acceleration is referred to as acceleration due to gravity. It can be measured using a simple pendulum and its value is 10m/s²

__Equation of motion under gravity.__

- From linear motion equation

V = U + gt

h = ut + ½ gt²

v² = U² + 2gh

- If the body is thrown upwards, its velocity decreases up to zero at maximum height. It is said to be decelerating hence g is negative. Equation for body moving upwards.

V = U – gt

h = ut – ½ gt²

V² = U² – 2gh

__The projectile motion.__

- Is a motion that is made of two independent motions, horizontal and vertical motion.
- Is a motion that is made of two independent velocity and one acceleration due to gravity. The horizontal motion haz no acceleration.
- The body that is carrying the projectile motion is called a projectile and the path that the body follows is called a trajectory path.

- The horizontal distance covered by the body is called a range.

__Equation of projectile motion.__

** Horizontal motion.**

- Has no acceleration a = 0 or g = 0

R = ut

** Vertical motion.**

- Has acceleration due to gravity g.
- Initial velocity is 0.

V = U + at V² = U² = 2gh

V = gt V² = 2gh

h = ut + ½ gt²

h = ½ gt²

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