The relation between the time t and position x for a particle
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The question seems to be incorrect.
t=px2 = qx must be t = px2 + qx
px2 + qx - t = 0
=> x = {-q + √(q2 + 4t)}/2p
=> x = -q/2p + 1/2p√(q2 + 4t)
taking positive values
Differentiating w.r.t. t
=> dx/dt = (1/2p) 4/[2√(q2 + 4t)]
=> v = 1/{p√(q2 + 4t)} ----1
=> pv = 1/√(q2 + 4t) ---2
Differentiating eqn. 1 w.r.t. t
=> dv/dt = -2/p [1/√(q2 + 4t) ]3
=> a = -2/p[pv]3 …by 2
=> a = -2p2v3
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