What is Linear motion?. comprises of distance and displacement

Distance: Is the space between two points.

Displacement: Is the distance moved in a specified direction.

The S.I unit of distance and displacement is metre or m

Distance is a scalar quantity while displacement is a vector quantity.

Speed: Is the rate of change of distance. Or It is distance moved in a unit time.

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Velocity; is the rate of change of displacement. Or It is speed in a specified direction.

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The S.I unit of speed and velocity is metre per second. (m/s) or (ms-1).
Speed is a scalar quantity while Velocity is a vector quantity.

Differences between velocity and speed

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Types of velocities

initial velocity u’

Is the velocity with which a body starts motion in a given time interval.

Note;

  1. For a body starting from rest the initial velocity “u’ must be zero ie. u = 0 ms-1
  2. For a stationary body starting motion means that the body is starting from rest u = 0 ms-1
  3. For a body traveling with a certain velocity, x, the initial velocity for such a body will be x so, u = x ms-1 e.g. a car traveling at 20 ms-1, has u =20 ms-1

Final velocity v’
The velocity with which a body ends motion for a given time.
Note: if a body is brought to rest, then the final velocity is zero ie, v = 0m/s.eg; A body traveling at 20m/s is uniformly brought to rest in 2s. Then; v = 0m/s.
The units of velocity must include m/s or km/hr or cm/s.

Average velocity:

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Uniform velocity
Is the constant rate of change of displacement.
OR
Uniform velocity is when a body makes equal displacements in equal time intervals.
When a body moves with uniform velocity, initial velocity (u) must be equal to final velocity, v. i.e. V = u.
E.g. A car traveling with uniform velocity of 20m/s has u=20m/s. V=20m/s.

When a body moves with uniform velocity, its acceleration is zero. (i.e a = 0).

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Change in velocity = final velocity (V) – initial-velocity (U)
The S.I unit for change in velocity is m/s2 or ms-2.
Uniform acceleration
Uniform acceleration is the constant rate of change in velocity with time.

OR:
Uniform acceleration is when a body moves with equal change in velocity in equal time intervals.
When a body moves with uniform acceleration, the final velocity is not equal to initial velocity.

Example.
A car starts from rest and it accelerates to 10m/s. Calculate the change in velocity.
U=0m/s
V=20m/s Change in velocity=v−u

Change in velocity=20−0

=20ms−1

Note: the velocity to which a body is accelerating becomes the final velocity for that given time interval.

Differences between velocity and acceleration

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Equations Of Motion
The units of acceleration must always be m/s2 and units m/s or km/hr are for velocity.

1st Equation of motion
From the definition of acceleration.

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This is called the first equation of motion.

Example1
A car started from rest it accelerates uniformly for 5s at a rate of 4m/s2. Calculate the final velocity.

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Example 2.
A body starting from rest is accelerated to 30m/s in two seconds. Calculate the acceleration of the body.

Solution

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Example 3.
A body starts from rest and accelerated uniformly at 2m/s2 for 3s. Calculate the final velocity.
Solution

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Example 4.
A body traveling at 10m/s is accelerated uniformly for 3 seconds at 5m/s2. Calculate the velocity at the end of the third second.
Solution

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Example: 5.

A body traveling at 20m/s is accelerated for 4s at 5m/s2. Calculate the average velocity.
Solution

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Example: 5.
A car travels with a uniform velocity of 20m/s for 6s. Calculate its acceleration.
Solution

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Example: 6.
A car traveling at 90km/hr is uniformly brought to rest in 40 seconds. Calculate the acceleration.

solution

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