# Physics 9th: Motion | Speed and Velocity

## 9th Physics | Motion | Speed and Velocity

### SPEED

The speed of a body tells us how slow or fast that body is moving. speed of a body is the distance travelled by it per unit time

$\displaystyle \text{Speed}=\frac{\text{Distance}\,\,\text{Travelled}}{\text{Time}\,\,\,\text{Taken}}$

Speed is represented by ‘v’, distance by ‘s’ and time by ‘t’.

Therefore $\displaystyle v=\frac{s}{t}$

The S.I. unit of speed is $\displaystyle m{{s}^{-1}}$ (meter per second). It can also be represented as centimeter per second and kilometer per hour.

The speed of a running car is shown by an instrument called “SPEEDOMETER”. The distance travelled by the car is measured by another instrument called ODOMETER.

#### Average Speed

The average speed of a body is the total distance travelled divided by the total time taken to cover that distance.

$\displaystyle \text{Average}\,\,\text{speed}=\frac{\text{Total}\,\,\text{distance}\,\,\text{travelled}}{\text{Total}\,\,\text{time}\,\,\text{taken}}$

### Solution:

Speed of the car from     A to B = 40 km / hour

Average speed of car from     A to D = $\displaystyle \frac{AB+BC+CD}{1+1+1}$

= $\displaystyle \frac{40+20+90}{3}=\frac{150}{3}$

= 50 km / h

#### Uniform speed or constant speed

A body has a uniform speed if it travels equal distances in equal intervals of time, howsoever small the time intervals may be

For example

Speed (A to B) $\displaystyle =\frac{30}{1}$    = 30 km/hr

Speed (B to C)$\displaystyle =\frac{30}{1}$    = 30 km/hr

Speed (C to D) $\displaystyle =\frac{60}{2}$     = 30 km/hr

#### Non-uniform speed

A body has non-uniform speed if it travels unequal distances in equal intervals of time.

For example

Speed (A to B)$\displaystyle =\frac{30}{1}$    = 30 km/hr

Speed (B to C)$\displaystyle =\frac{20}{1}$    = 20 km/hr

Speed (C to D)$\displaystyle =\frac{10}{1}$      = 10 km/hr

### VELOCITY

Velocity of a body is the distance travelled by it per unit time in the given direction

$\displaystyle Velocity=\frac{Displacement\,\,(Dis\tan ce\,\,travelled\,\,in\,\,given\,\,direction)}{Time\,\,Taken}$

$\displaystyle v=\frac{s}{t}$

The S.I. unit of velocity is $\displaystyle m{{s}^{-1}}$

Therefore, 25 km/hr is SPEED and 25 km/hr towards North is VELOCITY.

The direction of velocity is the same as direction of displacement of the body.

#### Uniform velocity

A body is said to be in uniform velocity if it travels in a specified direction in a straight line and covers equal distances in equal intervals of time, howsoever small the time intervals may be.

Any change in velocity may occurs in three ways:

(a)    by changing the speed of the body

(b)    by keeping speed constant but changing the direction.

(c)    by changing both speed and direction

### Question:     An object is moving along a straight line and covers 500 m towards east in 10 seconds. Calculate speed and velocity of the object.

Solution:

If a person is moving due East, 500 m in 10 s, in a straight line.

$\displaystyle \text{Speed}=\frac{\text{distance}}{\text{time}}=\frac{\text{500}}{\text{10}}=\text{50}\,\,\text{m/s}$

$\displaystyle Velocity=\frac{Displacement}{Time}=\frac{500}{10}=50\,\,m/s$

Therefore when the direction remains the same, velocity and speed have equal magnitude

### Question:     An object is moving along a straight road and covers 500 m in 10 seconds it returns from there and reaches the starting point in 10 seconds. Calculate speed and velocity for the whole journey.

Solution:

In this case the person goes from A to B and then returns back to A.

$\displaystyle Speed=\frac{Distance}{Time}=\frac{500+500}{10+10}$

$\displaystyle =\frac{1000}{20}=50\,\,m/s$

$\displaystyle velocity=\frac{Displacement}{Time}=\frac{Distance\,\,travelled\,\,in\,\,a\,\,given\,\,direction\,\,(East)}{Time}$

= $\displaystyle \frac{500-500}{20}=\frac{0}{20}=0$ m/s

Therefore when there is a change in direction, velocity and speed have different magnitudes.

#### Average velocity

If a body has changing velocity, but the change is uniform, the average velocity can be calculated as

$\displaystyle Average\,\,velocity=\frac{Initial\,\,velovity+Final\,\,velocity}{2}$

It is also represented as

$\displaystyle \bar{v}=\frac{u+v}{2}$

where, $\displaystyle \bar{v}=$ Average velocity

u = Initial velocity

v = Final velocity

#### Note: Average speed of a moving body can never be zero, although average velocity of a moving body might be zero.

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