imagine-a-drone-with-mass-m-flying-in-a-circle-of-radius-r-its-speed-changes-ove

Question

Imagine a drone with mass m flying in a circle of radius r. Its speed changes over time according to atana_{tan} = a + $$bt^{2}$$, where a and b are constants and t is time in seconds. Starting with an initial speed v_{0} at t=0, find the formulas for the tangential force (FtanF_{tan}) and radial force (FRF_{R}) acting on the drone for any time t greater than 0.

Accepted Answer

Ftan =m(a+bt2),FR=m(v0+at+b3t3)2rF_{	ext{tan }}=m\$$left(a+bt^2$$ight),F_{R}=m\frac{\left($$v_0+at$$+\frac{b}{3}$$t^3$$\$$right)^2$$}{r}

Answer

Ftan⁡=m(at+12bt2), FR=m(v0+at+b2t3)2rF_{	an}=m\left(at+\frac{1}{2}$$bt^2$$ight),\ F_{R}=m\frac{\left($$v_0+at$$+\frac{b}{2}$$t^3$$\$$right)^2$$}{r}

Answer

Ftan⁡=mbt2, FR=m(v0+at2+b2t4)2rF_{	an}=$$mbt^2$$,\ F_{R}=m\frac{\left($$v_0$+at^2$$+\frac{b}{2}$$t^4$$\$$right)^2$$}{r}

Answer

Ftan⁡=mat2, FR=m(v0+b2t2)2rF_{	an}=$$mat^2$$,\ F_{R}=m\frac{\left($$v_0$$+\frac{b}{2}$$t^2$$\$$right)^2$$}{r}