Here\'s the problem: \"A particle with mass m moves subject to the force F(vecto
ID: 1954226 • Letter: H
Question
Here's the problem:"A particle with mass m moves subject to the force F(vector) = (bt^2)x-hat + (f(sub zero))y-hat, where m, b, and f(sub zero) are known positive constants. The initial coordinate values are: x(0) = y(0) = z(0) = 0 and the initial velocity constants are: x-dot(0) = z-dot(0) = 0 and y-dot(0) = v(sub zero). Find the equations of motion and then solve them to find the coordinates as a function of time."
I've found the equations of motions to be mx(double-dot) = bt^2, my(double-dot) = f(sub zero), and mz(double-dot) = 0.
Also, the coordinate as a function of time for z is z(t) = 0. But I don't know how to find x(t) and y(t). Any help would be appreciated!
Explanation / Answer
m d^2/dt^2 = b t^2 dx/dt = b t^3 / (3 m) + C1 C1 = 0 since dx/dt = 0 at t = 0 x = b t^4 / (12 m) + C2 C2 = 0 since x = 0 at t = 0 Now find y in the same manner m d^2 y / dt^2 = f dy/dt = f t / m + C1 = f t + V0 since dy/dt = V0 at t = 0 y = f t^2 / (2 m) + V0 t + C2 C2 = 0 since y = 0 at t = 0 y = f t^2 / (2 m) + V0 t