Second part of Newton's first law and the second law is in concern with acceleration and force. This was precursored by Galileo Galilee just a generation before Newton.

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ACCELERATION
CM [010] Galileo’s

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. . . it will change its state of motion only and only when
it is compelled to do so by forces impressed on it.
Part 3 of Newton’s First Law
Part 3 of Newton’s First Law spells the relation between state of motion and force:
The right place for this part should be a part of the second law where it would
probably read:
Force changes the state of motion [of a particle].
However, this is enough for us to start to discuss on a new state of motion.

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The States of Motion
Rest = Motionless = Constant rest In constant Motion of velocity v.
The states of motion of an object can be summarized as rest and being in motion at
any speed as described by Part 1 and 2 of Newton’s First Law.

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The States of Motion
Velocity start from 0 to any speed 𝑣𝑣.
Object accelerated.
In raising the object at rest to a state of motion, we have acceleration.
Time
Velocity

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Acceleration
Actually, when an object picks up speed, it accelerates. If it slows down it
is said to decelerate. However, for convenience in general discussion, any
motional change is said to be in acceleration.
Acceleration Deceleration

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Acceleration due to
Gravity
The most familiar event of
acceleration is in free falling
caused by gravity. The earth
pulls the object and it falls
straight to the ground. It can be
seen that the rate of falling
varies. It increase steadily with
height. The object will fall faster
and faster until it hits the
ground. That is, the rate of
acceleration increases on time,
the longer an objects falls, the
greater acceleration it will
reach. The final velocity will be
tremendous.

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Rate of Free Fall
We know that things fall down because of the force of gravity. But Galileo did not
yet have the concept of gravity at the time. He took falling for granted and
concentrated on measuring how fast things can fall.

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Galileo Measured
Acceleration
Galileo used many devices to study constant motion
and acceleration. One of the major gadgets he used
was a ramp. The ramp would slow down the rate of
fall to make measurement manageable. He could
vary the slope of the ramp so that the speed of a ball
rolling down the ramp can be adjusted. The less
incline was the ramp, the slower would be the speed
of the ball, making it easier for timing purpose.

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Galileo Demonstrated his Ramp Experiment

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Equation for Acceleration
Over a period of 20 years, Galileo observed the motions of objects rolling down in
various inclination. By measuring the distance a ball rolled down the ramp in each
unit of time with water clocks or other timing devices. Galileo concluded from his
experiments that if an object is released from rest and gains speed at a steady
rate, then the total distance, 𝑑𝑑, travelled by the object is proportional to the
square of the time that it took in motion with g as the acceleration constant:
𝑑𝑑 ∝
1
2
𝑔𝑔𝑔𝑔2
Thus the first correct concept of accelerated motion was born.

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Geometric Representation of Acceleration
Since in acceleration, the velocity
changes from time to time. The graph
of acceleration is different from that of
velocity. The distance 𝑑𝑑 travelled by a
particle at constant velocity 𝑣𝑣 is:
𝑑𝑑 = 𝑣𝑣Δ𝑡𝑡 =
Δ𝑥𝑥
Δ𝑡𝑡
× Δ𝑡𝑡 = Δ𝑥𝑥
The distance 𝑑𝑑 travelled by a particle
at constant acceleration 𝑎𝑎 is:
𝑑𝑑 =
1
2
Δv
Δ𝑡𝑡
× (Δ𝑡𝑡)2
Obviously the distance is greater than
constant motion due to increasing
speed.
Distance(space)
Time
Δ𝑥𝑥
Δ𝑡𝑡
𝑣𝑣 =
Δ𝑥𝑥
Δ𝑡𝑡
𝑎𝑎

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NEWTON’S 2ND LAW
To be continued on CM [011]:
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