Question # The relation between time ( t ) and distance ( x ) is ( t=a x^{2}+b x ) where a and ( b ) are consiants. The acceleration is

# The relation between time ( t ) and distance ( x ) is ( t=a x^{2}+b x ) where a and ( b ) are consiants. The acceleration is

( (A)-2 a b v^{2} )

(B) ( 2 b v^{3} )

( (C)-2 a v^{3} )

( (D) 2 a v^{2} )

Solution

( t=a x^{2}+b x )

( 1=(2 a x+b) frac{d x}{d x} Rightarrow V=frac{1}{2 a x+b} )

a) ( frac{v d v}{d x}=frac{-v 2 a}{(2 a x+b)^{2}}=-2 a v cdot v^{2} )

( =-2 a v^{3} )

option ( (c) )