A particle moves along the s-axis. Use the given information to find the position of the particle. v(t) = 8t3;
s(0) = 5.
s= integral v(t)
s= INT 8t^3 dt= 2t^4+ s(0)
To find the position of the particle, we need to integrate the velocity function with respect to time.
Given that v(t) = 8t^3, we can integrate this function to obtain the expression for the position function, s(t).
∫v(t) dt = ∫8t^3 dt
Using the power rule of integration, we can integrate each term separately:
= 8 * ∫t^3 dt
= 8 * (t^4/4) + C
Applying the initial condition s(0) = 5, we can determine the value of the constant C:
s(0) = 8 * (0^4/4) + C
5 = 0 + C
C = 5
So the expression for the position function becomes:
s(t) = 8t^4/4 + 5
Therefore, the position of the particle at any time t can be found by substituting the value of t in the expression s(t) = 8t^4/4 + 5.