Displacement y in metres of a body varies with time t in sec- as y - -23t2-16t-2How long does the body take to come to rest-

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Standard XII

Physics

Different Kinds of Motion

Displacement ...

Question

Displacement y (in metres) of a body varies with time $t$ (in sec.) as y $= \frac{- 2}{3} t^{2} + 16 t + 2$
How long does the body take to come to rest?

8 s

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10 s

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12 s

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16 s.

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Solution

The correct option is D 12 s
Given y $= \frac{- 2}{3} t^{2} + 16 t + 2$
If the object comes to rest , the the velocity of the object is zero
Therefore $\frac{d y}{d t} = 0$
$\frac{d y}{d t} = \frac{d (\frac{- 2}{3} t^{2} + 16 t + 2)}{d t} = 0$
$= \frac{- 4}{3} t + 16 = 0$
$t = 12 s$
Therefore, the body comes to rest in $12 s$ .

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Displacement y (in metres) of a body varies with time t (in sec.) as y =−23t2+16t+2How long does the body take to come to rest?

The correct option is D 12 sGiven y =−23t2+16t+2If the object comes to rest , the the velocity of the object is zeroTherefore dydt=0dydt=d(−23t2+16t+2)dt=0=−43t+16=0t=12sTherefore, the body comes to rest in 12s.

Displacement y (in metres) of a body varies with time $t$ (in sec.) as y $= \frac{- 2}{3} t^{2} + 16 t + 2$
How long does the body take to come to rest?