Question

In some appropriate units, time (t) and position (x) relation of a moving particle is given by \(t = \alpha x^2 + \beta x\). The acceleration of the particle is :

• A. \( -2\alpha v^3 \)
• B. \( 2\beta v^3 \)
• C. \( -2\beta v^3 \)
• D. \( -2\alpha \frac{v^3}{(2\alpha x + \beta)^2} \)

Hint:

When position is not directly given as a function of time, use the chain rule for differentiation to find velocity and acceleration. Remember that \(v = dx/dt\) and \(a = dv/dt = (dv/dx)(dx/dt) = v (dv/dx)\). Alternatively, \(a = d^2x/dt^2\).