The motion of a particle along a straight line is described by equation : x = 8 + 12 t - t3 Where x is in metre and t in second. The retardation of the particle when its velocity becomes zero, is:

  • Option 1)

    24 ms-2

  • Option 2)

    Zero

  • Option 3)

    6 ms-2

  • Option 4)

    12 ms-2

 

Answers (1)

As we learnt in

Introduction to Differentiation -

frac{d}{dx}left ( x^{n} 
ight )={n} x^{n-1}
 

- wherein

frac{d}{dx}left ( x^{5} 
ight )=left ( n=5 
ight )

Rightarrow {n}x^{n-1}

Rightarrow {5}x^{5-1}

Rightarrow {5}x^{4}

 

 

 

x=8+12t-t^{3}

v=\frac{dx}{dt}=12-3t^{2}

Put v=0            3t^{2}=12,            t=2 \sec

a=-6 \times 2=-12m/s^{2}

Retardation = 12m/s^{2}

Correct option is 4.


Option 1)

24 ms-2

Incorrect

Option 2)

Zero

Incorrect

Option 3)

6 ms-2

Incorrect

Option 4)

12 ms-2

Correct

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