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What is the instantaneous velocity of an object with position at time t equal to # f(t)= (t^2-8,tsqrt(t^2+3t-4)) # at # t=2 #?

Answer 1

Paisley Johnson

Velocity vector #v(t)=(2t, (t(2t+3))/(2sqrt(t^2+3t-4))+sqrt(t^2+2t-4))#, and so,

#v(2)=(4, 7/sqrt 6 + sqrt 6)=(4, 5.31)#, nearly.

The position vector #r=r(x, y)=(x(t), y(t))=(t^2-8, t sqrt(t^2+3t-4))=f(t).#

So, the velocity vector #v(t)=(x'(t), y'(t))#

#=f'(t)=(2t, (t(2t+3))/(2sqrt(t^2+3t-4))+sqrt(t^2+2t-4))#

So, #v(2)=(4, 7/sqrt 6 + sqrt 6)#.

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Answer 2

Aurora Alvarado

The instantaneous velocity of the object at ( t = 2 ) is ( (4, 4\sqrt{3}) ).

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Answer from HIX Tutor

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