Question

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Answer 1

Given :-

Position of Particle,

r = (t²+6)î + (t + 2)j

1. In this we will put the value t = 4s and t = 2s

r = [(4)² + 6]î + (4+2)j -[{ (2)² + 6}î + (2+2)j]/(4-2)

r = 12î + 2j/2

r = 6î + j

Now, differentiating r w.r.t dt.

v = dr/dt

v = d|r|/dt

v = √37 ms-¹

2. In this we will just use simple differentiations.

v = dr/dt

v = d(t²+6)î + (t+2)j/dt

v = (2t)î + j

v = (2 × 3 ) i + j

v = 6i + j m/s

Answer 2

I hope it helps

GIVEN:-

Position of Particle ,

r = ( t² + 6 ) i + ( t + 2 ) j

1. In this we will put the value t = 4s and t = 2s

r = [ ( 4 ) ² + 6 ] î + ( 4 + 2 ) j - [ { ( 2 ) ² + 6 } î + ( 2 + 2 ) j ] / ( 4-2 )

r = 12i+ 2j / 2

r = 6î + j

Now , differentiating r w.r.t dt .

v = dr / dt

v = dlrl / dt

v = √37 ms - ¹

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