Question

Use the given acceleration function and initial conditions to find the position at time f=1 a(t)=6i+8j+8k,v(0)=0,r(0)=4j

Answer 1

To find the position at time f=1, integrate the acceleration function twice using the given initial conditions v(0) = 0 and r(0) = 4j.

Step-by-step explanation:

To find the position at time f=1, we need to integrate the acceleration function twice. Given a(t) = 6i+8j+8k and the initial conditions v(0) = 0 and r(0) = 4j, we first integrate a(t) to find the velocity function v(t). Integrating again will give us the position function r(t). Here's how to do it:

1. Integrate a(t) with respect to time to find v(t): ∫6i+8j+8k dt = 6ti+8tj+8tk + C1
2. Use the initial condition v(0) = 0 to find C1 = -8k
3. Integrate v(t) with respect to time to find r(t): ∫(6ti+8tj+8tk - 8k) dt = 3t^2i+4t^2j+8tk-8kt + C2
4. Use the initial condition r(0) = 4j to find C2 = -8k
5. Now we have the position function r(t) = 3t^2i+4t^2j+8tk-8kt - 8k