Monday, February 28, 2011

Distance and displacement


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 )




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