Question

velocity of object V= x² - 8 x + 4 then time of which acceleration of object will be zero

Answer 1

Refer to the above attachment

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Answer 2

Answer:

At t = 4 sec the acceleration of the object will be 0 .

Explanation:

Provided that:

The velocity: V= x² - 8 x + 4 .... equation (i)

Differentiating equation (i) with respect to time(t) we get the acceleration (a) of object:

a = dV/dt that is given by:

$V= x² - 8 x + 4\\ a = \frac{dV}{dt} = \frac{d}{dt} (x² - 8 x + 4) \\ a = 0$

Equation (i) is time independent as there is no term of t; Hence there will be no acceleration with respect to time.

But if the equation would be:

V = t² - 8 t + 4 ..... equation (ii) ;

then the velocity and acceleration is dependent on time.

Differentiating equation (ii) with respect to time;

$V= t² - 8 t + 4 \: \: ...equation(ii)\\ a = \frac{dV}{dt} = \frac{d}{dt} (t² - 8 t + 4) \\ a = 2t - 8 \: \: ...equation(iii)$

Let the time is t' when the acceleration will be 0.

Then putting t = t' in equation (iii) we get;

$a = 2t - 8 \\ \\ |a|(at \: t = t \prime) = 0 \\so \: 2t \prime - 8 = 0 \\ or \: t \prime = \frac{8}{2} \: sec \\ = 4 \: sec$

So we get t' = 4 sec; that means at t = 4 sec the acceleration of the object will be 0 .