MOTION
DISTANCE(s): It is the length between two points. SI unit is the meter (m).
DISPLACEMENT(s): It is the distance travelled in a stated/specified direction. SI unit is meter (m).
SPEED (u, v): It is distance travelled per unit time. SI unit is meters per second (m/s).
VELOCITY (u, v): It is speed in a stated/specified direction. SI unit is meters per second (m/s).
ACCELERATION (a): It is the rate of change of velocity. SI unit is meters per second squared (m/s 2).
MOTION GRAPHS
1. DISTANCE – TIME GRAPHS
(a) CONSTANT(UNIFORM) SPEED
On a distance – time graph the gradient is numerically equivalent to the speed. Ie
G=v=
Where v = speed (m/s)
= change in distance ie s2 – s1
= change in time ie t2-t1
Therefore G=v=
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In the given example: G = v = = 10/5 = 2m/s
(b) AT REST
The object has stopped so the graph remains at the same level.
(c) NON CONSTANT(UNIFORM) SPEED
(i) INCREASING SPEED
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To determine speed at a point (instantaneous speed) draw a tangent to that point and calculate its gradient.
(II) DECREASING SPEED
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2. SPEED- TIME GRAPHS
(a) CONSTANT (UNIFORM) ACCELERATION
On a speed – time graph the gradient is numerically equivalent to the acceleration. Ie
G=a=
Where a = acceleration (m/s2)
= change in speed ie s2 – s1
= change in time ie t2-t1
Therefore G=a=
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In the given example: G = a = = 10/5 = 2m/s2
(b) CONSTANT SPEED
The speed is not changing so the graph remains at the same level
(c) AT REST
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The object is not moving so the graph remains on the time axis
(d) NON CONSTANT ACCELERATION
(I) INCREASING ACCELERATION
To determine acceleration at a point (instantaneous) acceleration, draw a tangent to that point and
calculate its gradient.
(ii) DECREASING ACCELERATION
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(e) CONSTANT DECELERATION
G=a=
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In the given example: G = a = = 40/-10= -4m/s2
The value of the acceleration is negative and this shows that the object is decelerating.
NOTE: On a Speed – Time graph the area under the graph is numerically equivalent to the distance
travelled.
Example 1: The following graph shows motion of a car
Calculate the distance travelled by the car in the first 4s.
S = ½ bh = ½* 4s*20m/s = 40m.
EQUATIONS OF LINEAR MOTION
These equations are used for motion along a straight line. They show how velocity, displacement,
acceleration and time are related to one another.
SYMBOLS USED
s– displacement (m)
t – time(s)
a - acceleration (m/s2)
u – initial velocity (m/s)
v – final velocity (m/s)
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EQUATIONS
V = u + at _____________ (1) i.e Final velocity = Initial velocity + Gain in velocity.
Where = average velocity = , so equation (2) can be expressed as:
S =( ------------------------------------(2)
Substituting equation 1 into equation 2 we get
S= = = +
S = ut + ½ at2 ------------------------------------- (3)
Equation 1 can be expressed as t=
Substituting the above expression into equation 2 we get
S=( )= =
S= ------------------------------------------------ (4)
FALLING BODIES
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We are held to the ground by the force of gravity. Objects released from a height h above the ground fall
downwards because of the force of gravity. As objects fall downwards from a height h they accelerate.
The acceleration is called acceleration due to gravity g. The value of g is around 9.87 m/s2 but the value is
rounded to 10 m/s2. In equations of motion g replaces a when dealing with falling or rising objects. The
value of g is assigned a positive (+) value for falling objects and a negative value for rising objects.
TERMINAL VELOCITY AND FREE FALL
When an object is released from a height h, it accelerates towards the earth’s surface. On its way
downwards air resistance increase drastically due to the object’s surface area.
The net force (resultant) which gives the object its acceleration decreases as:
FR (resultant force) = w(mg) - ff . Therefore the acceleration of the object decreases. Eventually we reach
a point where w(mg) = ff ie the weight and air resistance equivalent. The resultant force F R will become
zero.
Using Newton’s 2nd law (FR = ma) if FR equals to zero it means acceleration will also be zero therefore
the object falls at a constant velocity called Terminal Velocity.
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TERMINAL VELOCITY: It is when an object falls at a constant (uniform) velocity.
OBJECTS FALLING IN A LIQUID
When the ball is released it accelerates downwards due to its weight. As the ball accelerates downwards,
the upward viscous force FV (internal friction force in a liquid) increases until eventually the viscous force
is equivalent to the weight of the ball. When the forces acting on the ball balances it falls at a constant
velocity called terminal velocity.
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