The relation between time t and distance x is t = ax^2 + bx, where a and b are positive constants. Its acceleration is?

Dear Vishrant

t = ax^2 + bx

differentiate w.r.t t

1= 2ax dx/dt + b dx/dt

1= (2ax+b)dx/dt

dx/dt = 1/(2ax+b)

again differentiate

d²x/dt² = -1/(2ax+b)²  (2adx/dt)

 a= -1/(2ax+b)²   * 2a/(2ax+b)

 a = -2a/(2ax+b)³

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Dear Student

Please see the solution in the attachment.
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Yash Chourasiya