Suppose a(t)=18t+8, v(1)=15, and s(1)=19. Find s(t).
To find s(t), we need to integrate v(t) to find the expression for s(t).
Given:
v(t) = a'(t) = 18
v(1) = 15
We can now integrate v(t) to find s(t):
s(t) = ∫v(t)dt = ∫18dt = 18t + C
To find the value of C, we use the initial condition:
s(1) = 19
19 = 18(1) + C
19 = 18 + C
C = 19 - 18
C = 1
Therefore, the expression for s(t) is:
s(t) = 18t + 1