I have a kinematic problem where a=3sin8t. I have no idea how to solve it, since acceleration is not constant? Or is it? It asks me to locate the position of the body at t=6s given t=0 the object is at x=7m and v=0

Question

noelgreco · Answer

Acceleration is the derivative of velocity which is the derivative of position.  You have to go backwards (antidifferentiate) twice using the initial values given as the constants of integration.

anonymous · Answer

the problem is that I am only given 1 initial condition. The first integral gives me an unknown constant, and the second one makes this constant dependant of the variable, plus another new constant. This means I am only able to solve the first constant with the initial conditions (t=0, x=7) but I am unable to find the other constant.

noelgreco · Answer

If you integrate twice, you'll have two constants of integration, $$v _{0}  and  x _{0}$$

Plug a 0 in for t in your final equation for x, plug in your two constants of integration. and solve.

noelgreco · Answer

Sorry, plug in a 6 for t.

noelgreco · Answer

what did you get as formulas for v and x?

noelgreco · Answer

I'm cutting the grass - back .5 hr