Imagine a drone with mass m flying in a circle of radius r. Its speed changes over time according to $a_{tan}$ = a + bt², where a and b are constants and t is time in seconds. Starting with an initial speed v₀ at t=0, find the formulas for the tangential force ($F_{tan}$ ) and radial force ($F_R$ ) acting on the drone for any time t greater than 0.

• A. $F_{\tan }=m\left(at+\frac{1}{2}bt^2\right),\ F_R=m\frac{\left(v_0+at+\frac{b}{2}t^3\right)^2}{r}$
• B. $F_{\tan }=mbt^2,\ F_R=m\frac{\left(v_0+at^2+\frac{b}{2}t^4\right)^2}{r}$
• C. $F_{\text{tan }}=m\left(a+bt^2\right),F_R=m\frac{\left(v_0+at+\frac{b}{3}t^3\right)^2}{r}$
• D. $F_{\tan }=mat^2,\ F_R=m\frac{\left(v_0+\frac{b}{2}t^2\right)^2}{r}$

Answer: (C)