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The position of a particle is defined by...

The position of a particle is defined by `vec r = 2sin((pi)/(4))t hati + 2cos((pi)/(4))t hatj+3t hatk` , where 't' is in seconds. Then distance travelled by particle in 2 second motions is. `[use pi^(2) = 10]`

A

`sqrt(32)m`

B

`sqrt(46)m`

C

`sqrt(56)m`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
The position …………
`vecr = 2sin(pi)/(4)t hati+2cos((pi)/(4))t hatj+3t hatk`
velocity `= vecv= (pi)/(2)cos ((pi)/(4)t)hat I - (pi)/(2)sin((pi)/(4)t)hatj+3hatk`
speed `=|vecv|= sqrt(((pi)/(2)cos((pi)/(4)t))^(2) + (-(pi)/(2)sin((pi)/(4)t))^(2)+9)`
speed `= v= sqrt((pi)/(4)^(2)+9)`
`v = (sqrt(46))/(2)`
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