Question

Let s(t) represent the position of a particle at time t, v(t) is the velocity and a(t) is the acceleration. What is the value of v(9) for the following:

Given that the acceleration of the particle at time t is a(t) = -3t^2+ 3t + 10 and that its position when t = 1 is s(1) = 1 and when t = 2 is s(2) = 1.

Answer 1

a(t) = -3t^2 + 3t + 10
v(t) = -t^3 + 3/2 t^2 + 10t + a
s(t) = -1/4 t^4 + 1/2 t^3 + 5t^2 + at + b
given s(1)=1 and s(2)=1,

1 = -1/4 + 1/2 + 5 + a + b
1 = -4 + 4 + 20 + 2a + b

a = -59/4, b = 21/2

v(9) = -729 + 243/2 + 90 - 59/4 = -2129/4