1 Answer

Dietpixel · Answer 1 · 2023-10-14T18:47:33+0000

Answer:

$a=36\: \sf ms^(-2)$

Explanation:

$\textsf{Displacement}\:x=4t^3-27t+8$

$\implies \textsf{Velocity}\:v=(dx)/(dt)=12t^2-27$

$\implies \textsf{Acceleration}\:a=(dv)/(dt)=24t$

At the moment the direction of motion of P reverses, the velocity of P will be zero. Therefore, find the value of t when v = 0:

$\implies v=0$

$\implies 12t^2-27=0$

$\implies t^2=(27)/(12)=\frac94$

$\implies t=\pm√(\frac94)=\pm\frac32$

As time is positive, P reverses when t = 3/2 s

To find acceleration at this time, simply substitute the found value of t into the equation for acceleration:

$\implies a=24(\frac32)$

$\implies a=36\: \sf ms^(-2)$

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