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SPEED, DISPLACEMENT AND VELOCITY

CONTENTS Time
  Distance
  Speed
  Displacement
  Velocity
  Mandatory Experiment: To Measure Velocity with a Ticker Timer

Time

The unit of time is the second. Time is a scalar quantity.

1 ms = 1 millisecond = 1x10-3  seconds.

1 cs = 1 centisecond = 1x10-2 seconds.

Distance

The unit of distance is the metre. Distance is a scalar quantity.

Small distances are measured with a vernier calliper or a micrometer.

VERNIER CALLIPERS

Click here to see how to read the vernier callipers.
MICROMETER

Click here to see how to read the micrometer.

1 mm = 1 millimetre = 1x10-3  metres.

1 cm = 1 centimetre = 1x10-2 metres.

1 km = 1 kilometremetre = 1x103  metres

SPEED

Speed is the rate of change of distance with respect to time.

The unit of speed is the metre per second, ms-1.

REMEMBER:

Click here for an explanation.

Click here for some examples of the speed triangle.

Example

Svetlana Masterkova of Russia ran 1,000 m in 2 min 28.98 sec
in Brussels, Belgium, on August 23, 1996.
Calculate her average speed.

Answer

 

Example

The highest speed ever achieved on a bicycle was 268.831 km/h (167.043 mph), by Fred Rompelberg (The Netherlands) at Bonneville Salt Flats, Utah, USA, on October 3, 1995.
His record attempt was greatly assisted by the slipstream from his lead vehicle.
(i) Calculate this speed in ms-1.
(ii) Supppose this speed is maintained for 2.5 seconds.
      Calculate the distance travelled in this time.

Answer
(i)

(ii)

DISPLACEMENT

Displacement is distance in a given direction.

Displacement is a vector quantity.

The symbol for displacement is s.

The unit of displacement is the metre.

Example

A car travels 3 km East then 4 km North.
(i) Find the total distance travelled.
(ii) Find the magnitude of the displacement.

Answer
(i) d = 3 + 4 = 7 km

(ii) The magnitude of the displacement is given by the distance from start to finish.
           
     From Pythagoras' theorem:
    


 

Example

The Earth travels in an approximately circular orbit around the Sun.
The radius of its orbit is 1.496x1011 m.
(i) Find the distance the Earth travels in one year.
(ii) Find the magnitude of its displacement in one year.

Answer
(i) In one year, the Earth orbits the Sun once.
    This gives a total distance of
    

(ii) Since the Earth returns to the same place, the start finish distance is zero.
     Thus the displacement s = 0 m.

VELOCITY

Velocity is the rate of change of displacement with respect to time.

The unit of velocity is the metre per second, ms-1.

Velocity is a vector. Its symbol is v or u.

Example

 

A person walks from a to b and then to c in a time of 3.4 seconds.
(i)  Find their average speed.
(ii) Find their average velocity.

Answer
(i)

MANDATORY EXPERIMENT:
TO MEASURE VELOCITY WITH A TICKER TIMER.

Apparatus

Ticker timer, ticker tape, trolley, runway.

Method

Set up apparatus as in diagram.

The timer prints 50 dots per second.

Start the timer and give the trolley a push.

The trolley should move along the runway with a constant velocity.

Result

The image above shows a section of ticker tape.

Mark a starting line. Count five dots and mark a finish line.

Measure the distance, s, between the lines. Here s = 3 cm.

Since it takes 1/50 seconds to print each dot, it took a time t = 5/50 = 0.1 seconds to print the five dots.

Thus the velocity of the trolley is given by v = s/t = 3/0.1 = 30 cms-1.

Source of Error.

Friction may cause the trolley to decelerate.

Solution

  1. Oil the wheels of the trolley.
  2. Tilt the runway to compensate for any remaining friction.

Source of Error

The ticker timer may skip, i.e. some dots may not print out.

Solution

Adjust the spring on the ticker timer.