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Distance travelled

- Distance travelled by the object is the length of the path travelled by the object
- It is a scalar quantity
- It's S.I unit is meters

Displacement

- It is the shortest distance between the initial and final position of an object or it can also be defined as the measure of the straight line connecting the initial position and final position of an object.
- It is a vector quantity
- Its S.I unit is meters

Examples

1.A boy walks from point A to another point B in a linear direction for 10 m. What is his displacement and distance travelled?

Ans: Displacement = Distance travelled = 10m (since the object moves in linear direction)

2. A boy walks from point A to another point B in a linear direction for 10m and returns back to A. What is his distance travelled and displacement?

Ans: Distance travelled = AB + BA = 10 + 10 = 20 m and displacement = zero

3. A boy walks from point A to another point B in a linear direction for 10m and returns back to another point C. If A happens to be the midpoint of BC what is his distance travelled and displacement?

Ans: His distance travelled = AB+BA+AC = 10+10+10 = 30m

His displacement = AC = -10m (since it is negative displacement)

4. A girl starts from her house in her bicycle to go to her friend’s house. She rides through a street of length 300m from east to west and takes a right turn and rides for further 400m to reach her friend’s house. Calculate how far her friend’s house is from her house and what is her displacement?

Ans: The total distance travelled by the girl = 300 + 400 = 700m

Her displacement = the hypotenuse of the right triangle whose other sides are 300m and 400m

= √300^{2} + 400^{2} = 500m

5. A farmer while throwing pesticides on his square field of area 400 sqm walks along the foot path laid on the perimeter of the field. He walks from one corner of the field to diagonally opposite side of the field. What is his total distance travelled and his displacement?

Ans: His distance travelled = Sum of the two adjacent sides = 20+20 = 40m

His displacement = Length of the diagonal = √20^{2}+20^{2} = 20√2 m

16.A cyclist travels along the circumference of a circular field of radius 500m with a uniform speed. What is his distance travelled and his displacement when he subtends an angle of 60°, 90°, 180°, 270°, 300° and 360° from his initial position.

Ans: (i) __When he subtends an angle of 60° with respect to the center of the circle__

His distance travelled = Arc length of the circle from his starting position to final position

=1/6^{th} of the circumference = 1/6 x 2 x π x r = 523.33 m

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