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Byju's Answer

Standard XII

Physics

1st Equation of Motion

The relation ...

Question

The relation between time t and displacement is x is t = ax²+bx

Where a and b are constants. Find the relation between acceleration and velocity.

NOTE:I have a word with one of the subject experts named Aldin D Sousa.so, please him give the explanation.

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Solution

So, if t = ax^2+bx
then, 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 = -2av ³

Where V is the Velocity.

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