If the relation between time and position of a particle is given by t = Ax2 + Bx, where A and B are constant, then find the acceleration of the particle.
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t = ax2 + bx,
=> Differentiate both side with respect to time (t) ,
=> dt/dt = 2ax.dx/dt + b.dx/dt
=> 1 = 2axv + bv ,
=> v.(2ax + b) = 1 ,
=> (2ax + b) = 1/v,
=> Again differentiate both side with respect to time (t),
=> 2a.dx/dt = -v-2 . dv/dt ,
=> 2av = v-2 . acceleration,
=> acceleration = -2av3.
=> Differentiate both side with respect to time (t) ,
=> dt/dt = 2ax.dx/dt + b.dx/dt
=> 1 = 2axv + bv ,
=> v.(2ax + b) = 1 ,
=> (2ax + b) = 1/v,
=> Again differentiate both side with respect to time (t),
=> 2a.dx/dt = -v-2 . dv/dt ,
=> 2av = v-2 . acceleration,
=> acceleration = -2av3.
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