Figure shows a boy cycles from A to B, and then from B to C.

i ) Calculate the distance travelled by the boy and the displacement of the boy.

ii ) Calculate the speed and the velocity of the boy if the boy took 10 s to cycle from A to B and then to C.

iii) then the boy travelled back to A from C, calculate the total distance and displacement travelled by the boy.

Tips to answer this question :

Distance is the

__actual distance that was covered__

Distance depends on the path, from point A --> B --> C in the figure.

Distance (symbol d) does not have a direction, so it is a scalar . It always positive

Displacement (symbol s) is the

__shortest distance__from the starting point to the endpoint.

Distance independent of path taken , from point A to C in the ﬁgure.

Displacement has direction and is therefore a vector. It can be positive or negative

Speed is rate of

__change__of

__distance__.

__Speed is scalar__quantity

Velocity is rate of

__change__of

__displacement__. Velocity vector quantity.

Answer :

Distance from A to B and then to is

3 m + 4 m

= 7 m

Displacement from A to B and then to C is 5 m.

Speed from A to B and then to C

7 m / 10 s

= 0.7 m/s

Velocity from A to B and then to C is

5 m /10 s

= 0.5 m/s.

Distance from A-> B-> C -> B -> C is

3 m + 4 m + 3 m + 4 m

= 14 m

Displacement from A-> B-> C -> B -> C is

5 m - 5 m

= 0 m

( Because the boy's location is the same as his starting location, we use negative sign to indicate opposite direction )