Final answer:
To find A given d²(A)/(d)t² and initial conditions, integrate the first derivative and solve resulting equations using the initial conditions.
Step-by-step explanation:
To solve this problem, we can integrate the given second derivative of A(t) with respect to t twice. Let's start by finding the first derivative of A(t) using the given values. Given that A(t) = 2i + j, we have d(A)/(d)t = -i - 3k. Now, we can integrate the first derivative to find the original function A(t).
Integrating the first derivative, we get A(t) = -t + C1i + D1j - 3tk + C2, where C1, D1, and C2 are constants of integration. To find the values of these constants, we can use the given initial conditions at t = 0. Plugging in the initial conditions A(0) = 2i + j and d(A)/(d)t(0) = -i - 3k, we can solve the resulting equations to find the values of C1, D1, and C2.
By solving the equations, we find that C1 = 2, D1 = 1, and C2 = 0. Therefore, the equation for A(t) is A(t) = -t + 2i + j - 3tk.