The relation between time t and distance x is ax^2+bx, where a,b are constants

CBSE Class 11
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1

The relation between time t and distance x is ax^2+bx, where a,b are constants. the retardation is _____.

2

Please note that probably you forgot the LHS while writing the relation between t and x.
I think the correct equation would be t = ax2+bx. Please let me know if this wrong.
So, if t = ax2+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 = -2av3
Hence, retardation= 2av3