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The relation between time t and position x along x-axis is given by t = ax^2 + bx, where a and b are alpha and beta and they are constants. Prove that the retardation is 2aV^3, where V is the velocity at time t.

The relation between time t and position x along x-axis is given by t = ax^2 + bx, where a and b are alpha and beta and they are constants. Prove that the retardation is 2aV^3, where V is the velocity at time t.

Grade:11

2 Answers

vikas askiitian expert
509 Points
11 years ago

t = ax^2 + bx..............1

differentiate eq 1 wrt t

dt/dt = adx^2/dt + bdx/dt                    (dx/dt =V )

1=a(2xV) + bV...........2

again differnetiate wrt t

0=2a(xA+V^2)  + bA                          (dV/dt =A (retardation) )

A=-2Av^2 /2ax+b.................3

put the value of x in 3

A=-2Av^3

approve my ans if u like

NIKHIL GARG
38 Points
11 years ago

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