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Question

The relation between t and distance x is t=ax2+bx where a and b are constants. Express the instantaneous acceleration in terms of instantaneous velocity.

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Solution

t=ax2+bx1=2axdxdt+bdxdt1v=dxdt=1(2ax+b)(2ax+b)=1v2
differentiating1 w.r.t t
0=2axd2xdt2+2adxdt+bd2xdt22av=(2ax=b)dxdt2
using equation 2
d2xdt2=ains=2av2

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