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Question: The relation between time t and distance x is t = ax<sup>2</sup> + bx where a and b are constant. Th...

The relation between time t and distance x is t = ax2 + bx where a and b are constant. The acceleration is

A

-2abv2

B

2bv3

C

– 2av3

D

2av2

Answer

– 2av3

Explanation

Solution

t = ax2 + bx or dt/dx = 2ax + b

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

dvdt=−2a(2ax+b)2dxdt=−2a(2ax+b)3=−2av3\frac{dv}{dt} = \frac{- 2a}{(2ax + b)^{2}}\frac{dx}{dt} = \frac{- 2a}{(2ax + b)^{3}} = - 2av^{3}.