Motion In Straight Line

Motion is the change of position of an object from one place to another. There are two types of

motions;  i.Circular  motion-Is the motion  of  an  object in a circle. Examples;  a/.  motion  of the

electron around the nucleus of an atom b/.r evolutionary movement of the earth around the sun.

ii.Linear motion-Is the motion of an object in a straight line.

Distance and Displacement

Difference between Distance and Displacement

Distinguish between Distance and Displacement

Distance  Is  the  length  between  two  points  or  two  objects.It  is  a  scalar  quantity  i.e.  it  has  a

magnitude only but no direction. Its symbol is X or S and the SI unit is meter (m). Other units

used are Kilometer (km) and Centimeter (cm)

Displacement  Is  the  distance  in  a  specific  direction.  It  is  a  vector  quantity  i.e.  it  has  both

magnitude and direction.

Differences between distance and displacement

Distance

Displacement

Is the length moved by an object between two points  Is the distance in a specific direction

It is a scalar quantity

It is a vector quantity

The SI Units of Distance and Displacement

State the SI units of Distance and Displacement

The symbol for distance is X or S and the SI unit is meter (m). Other units used are Kilometer

(km) and Centimeter (cm)

The standard unit of displacement in the International System of Units ( SI ) is the

meter

(m).

Speed and Velocity

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Difference between Speed and Velocity

Distinguish between Speed and Velocity

Speed

Speed is the distance moved by an object in a unit time or is the rate of change of distance . It is a

scalar quantity.

Velocity

Velocity  is  the  displacement  moved  by  an  object  per  unit  time  or  is  the  rate  of  change  of

displacement. It is a vector quantity and its symbol is U or V.

Formula for speed and velocity

Speed(velocity) = Distance/displacement x time taken

X = Vt

Note:

36km/h = 10m/s

Differences between speed and velocity

Speed

Velocity

Is the rate of change of distance  Is the rate of change of displacement

It is a scalar quantity  Is a vector quantity

The SI Unit of Speed and Velocity

State the SI unit of Speed and Velocity

The SI unit of speed and velocity is meter per second (m/s). Other units are Km/h or cm/s

The Average Velocity of a Body

Determine average velocity of a body

Types of velocity

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1.

Initial velocity, U

– Is the velocity of a body at the start of observation

2.

Final velocity, V

– is the velocity of a body at the end of observation

3.

Average velocity

–is the average or mean between initial and final velocity or is the ratio

of the total displacement to the total time.

4.

Uniform  or  constant velocity

Is  the  one  whereby  the  rate  of  change  of displacement

with time is constant.

5.

Absolute  velocity

is  the  actual  velocity  of  a  moving  object  recorded  by  a  stationary

observer

6.

Relative velocity

is the velocity of a moving object recorded by a moving observer .

7.

Instantaneous velocity

is the velocity of a moving object recorded at any time.

Acceleration

Acceleration  is  the  rate  of  change  of  velocity  or  is  the  change  in  velocity  per  unit  time

Mathematically. Acceleration, a = (final velocity, v – initial velocity, u)/time, t

Velocity Time-graph

Interpret velocity time-graph

This is velocity against time graph. Consider a body accelerating uniformly from rest to a certain

velocity v within time t. This can be represented graphically as shown below;

Distance

The distance x moved by the body is given by the area under the curve.

In this case is the area of triangle OBC.

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Acceleration.

The acceleration is given by the slope of the triangle OBC.

The Acceleration of a Body

Determine the acceleration of a body

Example 1

A car starts from rest and accelerates to a velocity of 120m/s in one minute. It then moves with

this speed for 40seconds finally decelerates to rest after another 2 minutes. Calculate;

a.

the distance travelled

b.

the total time taken for the whole motion

c.

the deceleration

d.

the average velocity

Soln

1st stage; acceleration u =0, v = 120m/s,t1 =1min=60s

2nd stage; uniform vel u=v=120m/s,t2=40s

3rd stage; Deceleration u=120m/s,v=0,t3=2min=120s

1st stage; s =average vel x time = ( (120+0)/2)60 = 3600m

2nd stage; s = vt = 120 x 40 = 4800m

3rd stage; s = average vel x time = ((v=u)/2)t = ((120+0)/2)120 = 7200m

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Total distance, s T =3600+4800+7200 =15600m

Total time taken = 60 + 40 + 120 = 220s

from v = u + at

120 = 0 + 60a

60a = 120

a = 2m/s.

Average velocity = total distance/time

va = 15600/220

va = 71m/s

The Concept of Retardation

Explain the concept of retardation

Deceleration (retardation) is the rate of decrease of velocity or is the decrease in velocity per unit

time. Uniform acceleration or retardation Is the one whereby the rate of increase or decrease of

velocity is constant or it doesn’t change.

Note;

when a body starts f rom rest or is brought to rest, its velocity is zero

when the velocity of a body is constant or uniform, its acceleration is zero

when the velocity of a moving object increases, its acceleration becomes positive

when the velocity of a moving object decr eases, its acceleration becomes negative called

retardation.

Equations of Uniformly Accelerated Motion

Equation of Uniformly Accelerated Motion

Derive equation of uniformly accelerated motion

There are three equations of motion;

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Newton’s first equation of motion

It is given by; v = u + at

whereby;

u = initial velocity

v = final velocity

a = acceleration

t = time taken

PROOF;

From the formula of acceleration; a = (v-u)/t

at = v – u at + u = v

v = u + at proved!

Newton’s second equation of motion

It is given by

whereas;

s=distance travelled

u=initial velocity

t=time taken

a=acceleration

PROOF;

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Suppose an  object  starts  from  rest  with  intial  vel,u  to  final  vel,v after  time t The  distance  ,S

moved is given by S = Average vel x time S =( (u+v)/2)t

Substitute Newtons first eqn,gives; S = ((u+u+at)/2)t

S = ((2u+at)/2)t

S = ut + 1/2at. proved!

Newtons third equation of motion

It is given by V

2

= U

2

+ 2as

where v=final velocity; u =initial velocity; a = acceleration; s = distance covered.

PROOF

From Newton’s first eqn; v = u + at

Equations of Accelerated Motion in Daily Life

Apply equations of accelerated motion in daily life

Activity 1

Apply equations of accelerated motion in daily life

Motion under Gravity

The Concept of Gravitational Force

Explain the concept of gravitational force

The acceleration of a free falling body is known as the acceleration due to gravity denoted by g

and controlled gy gravitational force of the earth.

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When two bodies of different masses are released from a certain height h above the ground, they

will reach the  ground  at different times with the heavier one reaching earlier before the lighter

one.

The reason is  that the air resistance is  more  effective on lighter  bodies than in heavier bodies,

consequently this affect acceleration due to gravity in a reverse manner.

But  dropping a light  object and a heavy object in  a  vacuum  they will reach  the  ground at the

same time due to the absence of air resistance effect.

Consider the following two cases;

Case I

Consider a body falling freely from a certain height h and uses time t to reach the ground.

In this case: acceleration, a = acceleration due to gravity g

Initial velocity, u = 0

Final velocity, v.

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Case II

Consider a body thrown vertically upwards from the ground with an initial velocity u to a certain

height h and then comes back to the ground after time t.

In this case;

Acceleration, a = -g

Initial velocity = u

Velocity at h = 0

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Final velocity at the ground = v

Acceleration due to Gravity

Determine acceleration due to gravity

A simple pendulum is a small heavy body suspended by a light inextensible string from a fixed

support and it is normally used to determine acceleration due to gravity.

It is made by attaching a a long thread to a spherical ball called a pendulum bob. The string is

held at a fixed at a fixed support like two pieces of wood held by a clamp and stand.

If the bob is slightly displaced to position B,it swings to and from going to C through O and back

to B through O. When the pendulum complete one cycle/revolution the time taken is called the

period of oscillation, T.

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Definitions

1.

Period ,T

is the time taken by the pendulum bob to complete one complete cycle.

2.

Angular displacement

is the angle made between the string and the vertical axis when

the bob is displaced to a maximum displacement.

3.

Amplitude

is the maximum displacement by which the pendulum has been displaced.

4.

Length

of  pendulum  is  the  length  of  the  string  from  the  point  of  attachment  on  the

wooden pieces to the canterof gravity of the bob.

From the experiments, it has been observed that, changing the weight of the bob and keeping the

same length of pendulum, the period is always constant provided that all swings are small though

they may be different in size.

The period T of the pendulum is given by;

Where; l = length of pendulum; g = acceleration due to gravity

Also

It  follows  that if we  plot a graph  of  l  against T. it  is going to be a straight  line with a slope

g/4

2

and y –intercept equal to 0.

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When the bob is raised to point B it will gain potential energy and the bob will swing due to the

conservation of energy from potential to kinetic energy.

At B and C all energy is P.E.

At O all energy is K.E.

P.E at B = K.E at O.

If the pendulum swung in vacuum the oscillations would have been continuous. But practically,

air friction  causes  losses of  energy  of the pendulum  bob.  That is  why  after a certain time the

oscillations cease.

The Application of Gravitational Force

Explain the application of gravitational force

Activity 2

Experiment

Aim:

Determination of acceleration due to gravity by using the simple pendulum.

Materials and apparatus:

A simple pendulum, stand, clamps and stop watch.

Procedures

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Tie a piece of thread to a brass bob(about 100g)

Suspend a bob with a thread between wooden pieces by clamping them on to a stand.

Pull  the  bob  slightly  to  one  side  and  release  the  bob.  Make  sure  the  bob  swings  50

complete oscillations.

To be more accurate, perform three measurements for each length l of the pendulum.

Repeat the procedures with l = 60cm and 50cm.

Record the results as in the table below. -Plot the graph of l against T

2

Results

Length, l (cm)  Time for 50 oscillations.  T (s)  T² (s²)

t

1

(s)  t

2

(s)  t

3

(s)  Average(s)

Observation

The graph obtained will be a straight line through the origin.

The slope of the graph is given by;

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From this equation, the acceleration due to gravity can be computed easily.

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