What is the position of the particle, s(t), at any time t? (Multiple Choice)

Question

The velocity of a particle moving along the x-axis is v(t)= 1/sqrt(t). At t=4, its position is 2

Choose 1 answer:

A. s(t)=2t^1/2

B. s(t)= 2t^(1/2) -2

C. s(t)= 2/3t^3/2

D. s(t)= 2/3t^3/2 -10/3

Answer 1

v = 1/t^1/2 and s(t) = ∫ v(t)dt so s = ∫₀^t v(t)dt + C s(t) = ∫₀^t 1/t^1/2 dt + C doing the integration s= 2t^1/2 +C.

Now uisng the initial condition s(4) = 2 2 = 2·4^1/2 +C or 2= 4 + C and C=-2 Therefore the answer is B.

S(t) = 2t^1/2 -2.