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A particle is moving such that its posit...

A particle is moving such that its position coordinates `(x, y)` are `(2m, 3m)` at time `t=0, (6m, 7m)` at time `t=2 s`, and `(13 m, 14m)` at time `t=5 s`.
Average velocity vector`(vec(V)_(av))` from `t=0` to `t=5 s` is

A

`(1)/(5)(13hat(i)+14hat(j))`

B

`(7)/(3)(hat(i)+hat(j))`

C

`(hat(i)+hat(j))`

D

`(11)/(5)(hat(i)+hat(j))`

Text Solution

Verified by Experts

The correct Answer is:
D
Average velocity, `upsilon_(av)=("Displacement"(Delta r))/("Time taken"(Delta t))`
Displacement in t = 0 to 5s is
`Delta r=(!3-2)hat(i)+(14-3)hat(j)=11hat(i)+11hat(j)`
`v_(av)=(Delta r)/(Delta r)=(11)/(5)(hat(i)+hat(j))`
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