Find the position function s(t) of a particle in motion if it is known that:

Question

Find the position function s(t) of a particle in motion if it is known that:

1. the particle's acceleration is constant with a(t)= -6 m/s²
2. the velocity of the particle at time t=2 is: -27 m/s
3. the position of the particle at time t=1 is: 8 m

Answer 1

v(t) = ∫a(t)dt = ∫(-6)dt = -6t + C

Since v(2) = -27, we have -12 + C = -27. So, C = -15

v(t) = -6t - 15

s(t) = ∫v(t)dt = ∫(-6t - 15)dt = -3t² - 15t + C₁

Since s(1) = 8, -18 + C₁ = 8. So, C₁ = 26.

s(t) = -3t² - 15t + 26