Inverse/implicit relationship between position and time
A question where time is given as a function of distance/position (or position is given implicitly), requiring implicit differentiation or algebraic manipulation to find velocity, acceleration, or their dependence on position.
The relation between time $t$ and distance x is $\mathrm{t} = a\mathrm{x}^2 + \mathrm{bx}$ where a and b are constants. The acceleration is (1) $-2abv^2$ (2) $2bv^3$ (3) $-2av^3$ (4) $2av^2$
The distance $x$ covered by a particle in one dimensional motion varies with time $t$ as $x ^ { 2 } = a t ^ { 2 } + 2 b t + c$. If the acceleration of the particle depends on $x$ as $x ^ { - n }$, where $n$ is an integer, the value of $n$ is $\_\_\_\_$