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

Physics 9th: Motion | Uniform and Non-uniform Motion

9th Physics | Motion | Uniform and Non-uniform Motion

UNIFORM MOTION

A body is said to have uniform motion if it travels equal distances in equal intervals of time, howsoever small the time interval may be

For example

This body is travelling 25 m in the first second, 25 m in the second and 25 m in the third second. It is therefore undergoing uniform motion.

NON-UNIFORM MOTION

A body is said to have non-uniform motion if it travels unequal distances in equal intervals of time

For example

If a body starts at A and acted upon by a force it initially travels slowly then it gains speed. It travels 5 m in the first second, 15 m in the second and 25 m in the third. As these are unequal distances, it is known as non-Uniform motion.