(c) Given, $\ x = at^{2} + bt + c$ $\Rightarrow \ (speed)\frac{dx}{dt} = 2at + b$ $\Rightarrow \ \ (acceleration)\frac{d^{2}x}{dt^{2}} = 2a$ $\therefore\$The particle will moving with Uniform acceleration.
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.