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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.

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

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**

**Types of velocities**

initial velocity **u’**

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

**Note;**

- For a body starting from rest the initial velocity “u’ must be zero ie. u = 0 ms-1
- For a stationary body starting motion means that the body is starting from rest u = 0 ms-1
- 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:**

**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).

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**

**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.

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.

**Example 2.**

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

**Solution**

**Example 3.**

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

**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**

**Example: 5.**

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

**Example: 5.**

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

**Example: 6.**

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

**solution**