Vectors and Scalars

Speed And Velocity

SPEED AND  VELOCITY

1.     A skier travels 3000m in 93s. Calculate her speed.

S = d ÷ t = 3000m ÷ 93 s = 32.26 m/s

2.     A cyclist travels 1000m in 75s. Calculate his speed.

S = d ÷ t = 1000m ÷ 75 s = 13.33 m/s

3.     A train travels 1200m in 80s. Calculate its speed.

S = d ÷ t = 1200m ÷ 80 s = 15 m/s

4.     A mouse walks 10m in 20s. Calculate its speed

S = d ÷ t = 10m ÷ 20s = 0.5 m/s

5.     Concord travels at 660m/s (twice the speed of sound in air at 0⁰C). How far will it travel in one minute?

d = s x t = 660 m/s x (1 x 60s) = 39600 m = 39.6 km

6.     To leave the Earth’s gravitational field a space vehicle must reach escape speed which is about 18 km/s. How high will the rocket be 34s after lift off? Has any human left the influence of the Earth’s gravitational field?

d = s x t = 18 km/s x 34s = 612 km

No – as the moon orbits the Earth

7.     The term light year is often misused. It is the distance light travels in one year. Given that light travels at 300 000 000m/s (3x 10⁸ m/s) how far is that light year?

1 light year or d = s x t = 3 x 10⁸ m/s x (365.25 days x 24 hr x 60min x 60s) = 9.47 x 10¹⁵ m

If you could travel at the speed of light (not possible) how long would it take you to travel that light year?

For you no time would pass. For those on earth 1 year would pass.

8.     A car travels at 35m/s on a motorway. How long will it take to travel that light year? (In years please)

t = d÷s = 9.47 x 10¹⁵ m ÷ 35 = 2.7 x 10¹⁴ s =  2.7 x 10¹⁴ s ÷ (356.25 days x 24 hr x 60 min x 60 s) = 85.6 million years

9.     A waiter walks at 2m/s. How long will it take him to reach your table 15m away and will your soup be cold when he gets there?

t = d÷s = 15 ÷ 2 m/s = 7.5 s       Yes, its Gazpacho

10.  A water ripple travels at 6 cm/s. How long will it take to travel 1m?

t = d÷s = 1 ÷ 6/100 m/s = 16.67s

11.  The average speed of a sprinter is about 11m/s. How long does she take to run the 100m?

t = d÷s = 100 ÷ 11 m/s = 9.09 s (a new world record!)

Compare this speed with a1500m runner who turns in a very respectable time of 3m 50s.

s = d÷ t = 1500m ÷ 230s s = 7.5 m/s

Why is there a difference? Oxygen debt due to build up of lactic acid in muscles

12.  A tennis player’s serve is measured at 50m/s. How long will it take to travel the length of a tennis court (23.8m)

t = d÷s = 23.8m ÷ 50 m/s = 0.48 s

The Steady Earth

I.      The Earth has a diameter of 12756km at the equator. Given it takes 23hrs and 56 minutes to revolve once how fast would you be travelling at the equator? (In m/s and km/h please.)

Distance travelled = circumference of Earth = pd = 3.142 x 12756 = 40 100 km = 4.01 x10⁷ m

Time taken =  23 hrs 56 min = {(23x60) + 56}min x 60s= 86160s

Speed = distance ÷ time = 40100km ÷ 23.93hr = 1676 km/h

Speed = distance ÷ time = 4.01 x 10⁷ m ÷ 86160s = 465.4 m/s

What stops you flying off into space? Gravity

We live some way north of the equator, do we travel as fast? No as we travel less distance in one rotation.

How fast would you be spinning if you were at the North Pole? 0

II.     The average distance from our planet to the sun is 149,503,000 km. The earth orbits the sun once every 365.25 days. How fast are we all going?

Distance travelled = circumference of Earth’s orbit = 2pr = 3.142 x 2 x149 503 000km

= 4.697 x 10⁹ km = 4.697 x 10¹²m

Time taken =  365.25 days= 365.25 x 24 = 87000 hr = 87000 x 60min x 60s= 3.132 x 10⁸s

Speed = distance ÷ time = 4.697 x 10⁹ km  ÷ 87000 hr = 54 000 km/h

Speed = distance ÷ time = 4.697 x 10¹²m ÷ 3.132 x 10⁸s = 1.5 x10⁴ m/s = 15 km/s = 465.4 m/s

(Assume the orbit is circular, it's not quite, we are slightly closer to the sun in January than July; if so why is it so cold? The seasons are caused by the tilt of the earth’s axis of rotation to the plane of its orbit)

III.    The sun and the whole solar system are on the move around the centre of our galaxy that is called The Milky Way. We are moving towards the constellation of Hercules at a leisurely 20.1 km/s. At this speed how long would it take to travel around the Earth?

Time = Distance ÷ speed = 40 100 km ÷ 20.1 km/s = 1995 s = 33 min

IV.   This is nothing the whole of our galaxy is on the move as the universe expands. We all move outward towards the constellation of Leo (only from our point of view) at 600km/s. How far have we travelled since you started this worksheet? 360 000km… but then it only took me 10 minutes

Information you may need

Velocity = distance/time            distance = speed x time            time = distance/velocity

Diameter of a circle = twice its radius (r)             circumference = 2pr       p = 3.142

Speed

Units

Quantities and Units