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}}

 

Question:     A body is moving along a straight line and covers 40 kms in first hour, 20 kms in second hour and 90 kms in third hour. Calculate the average speed of the whole journey.

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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