A particle is moving with the given data. Find the position of the particle.

Question

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A particle is moving with the given data. Find the position of the particle.

(a) v (t)=3t-1/(1+t^2), s(0)=1

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(b) a (t)=2sin t + 3cos t, s(0)=0, v(0)=2

Answer 1

b) a(t) = 2sint + 3cost,

s(0) =0 v(0) =2

integrate to get v(t)

v(t) = -2cost +3sint + C

v(0) = -2cos(0) + 3sin(0) + C = 2

-2 + 0 + C =2

C=4

v(t) = -2cost + 3sint +4

integrate to get s(t)

s(t) = -2sint -3cost +4t + K

s(0) = 0 - 3 + 0 + K = 0

K = 3

s(t) = -2sint -3cost +4t + 3