Speed - Velocity

Speed - Velocity

Speed

Recapitulation

In sixth standard we already studied about the speed in detail.

1 km/h = 5/18 m/s

How we got this ?

1 km = 1000 m

1 h = 3600 s

1 km / h = 1000 m / 3600 s = 5/ 18 m /s

Speed is the rate of change of distance .

Speed = distance /time

Unit is metre/second (m/s)

We can classify speed into two types.

Uniform speed

If a body in motion covers equal distances in equal intervals of time, then the body is said to be in uniform speed.

Non- uniform speed

If a body covers unequal distances in equal intervals of time, the body is said to be in non-uniform speed.

Average speed = total distance travelled / time taken to travel the distance.

Velocity

Velocity is the rate of  change in displacement.

Velocity (v) = displacement / time

SI unit of velocity is meter / second (m/s).

If an athlete in the diagram takes 25 s to complete a 200 m sprint event. Find her speed and velocity.

Speed           = distance / time

                      =200 / 25

                      =8 m/s

velocity = displacement /time

            =50/25

             =2 m/s

Uniform velocity

A body has uniform velocity, if it covers equal displacement in the same direction in equal intervals of time. E.g. light travels through vacuum.

Non uniform velocity

If either speed or direction changes, the velocity is non uniform. E.g. a train starting and moving out of the station.

Average velocity

Average velocity = total displacement / total time taken

E.g. Figure shows a car that travels 5 km due east and makes a U – turn to travel another 7 km. If the time taken for the whole journey is 0.2 h. Calculate the average velocity of the car.

Average velocity = total displacement/time taken. (taking the direction due east of point O as positive)

                  = (5–7)/0.2

                  = –2 / 0.2

                  = –10 km/h (or) –10 × 5/18 = 25/9

                  =   –0.28 m / s

The triangle method can help you to recall the relationship between velocity (v), displacement (d), and time(t).

       v = d / t , t = d / v, d = v × t

Answer the following questions:

* Calculate the velocity of a car travelling with a uniform velocity covering 100 m distance in 4 seconds.

Velocity  = Sistance / time = 100/4 = 25 m/s

* Usain Bolt covers 100 m distance in 9.58 seconds. Calculate his speed. Who will be the winner if Usain Bolt comepetes with a Cheetah running at a speed of 30 m/s?

Speed of Usain Bolt = 10.43 m/s

Speed of cheetah = 30 m/s

Cheetah will be the winner.

* You are walking along east covering a distance of 4 m, then 2 m towards south,then 4 m towards west and at last 2 m towards north. You cover the total distancein 21 seconds, what is your average speed and average velocity?

Total distance covered = 12 m

Total time taken =21 seconds

Average speed = Total distance covered / total time = 12m / 21 = 0.571 m/s

Average velocity = 0 m/s

12m / 21 = 0.571 m/s

Average velocity = 0 m/s

Average velocity is zero because the starting point and the finishing point is same

∴Displacement is zero so, average velocity is also

Average velocity = Total distance / time