Particle Movement and Positions

Question

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

a(t) = 2t + 9,    s(0) = 3,    v(0) = −3

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

v(t) = sin(t) − cos(t),    s(0) = 0

Please help me on Physics

Answer 1

I will work the first problem for you, and then you can apply the same kind of reasoning to solve the second problem.

a(t) = 2t + 9

v(t) = ∫a(t)dt = t² + 9t + c

v(0) = -3 ⇒ c = -3

v(t) = t² + 9t - 3

s(t) = ∫v(t)dt = t³/3 + 9t²/2 - 3t + c

s(0) = 3 ⇒ c = 3

s(t) = t³/3 + 9t²/2 - 3t + 3