Question

please solve this...

Answer 1

a) 16 m I think this is the right answer

Answer 2

Hope u like my process
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$\: \: \: \: distance \: \: travelled \: \: with \: \: time(t) \\ \: \: \: \: \: can \: \: be \: \: given \: \: as \\ \\ = > \it \: x = 40 + 12t - {t}^{3}$

=> It's velocity will be,

$= > v = \frac{dx}{dt} = \frac{d}{dt} (40 + 12t - {t}^{3} ) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = \bf \: 12 - 3 {t}^{2}$
Now,

=> Velocity turns to 0, if the body comes to rest.

$so..... \\ \\ = > \it v = 12 - 3 {t}^{2} = 0 \\ \\ = > 3 {t}^{2} = 12 \\ \\ = > {t}^{2} = 4 \\ \\ = > \bf \: t = 2.....since \: \: time \: \: cant \: \: be \: \: negative$

Now the distance travelled at 2 sec..

$= > \it x = 40 + 12(2) - {(2)}^{3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = \it \: 40 + 24 - 8 = \bf \underline{ 56 \: \: m}$
Now,..

Since the distance was travelled when time

$= > \it x = 40 + 12(0) - {(0)}^{3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: = \it \: 40 + 0 - 0 = \bf \underline{ 40 \: \: m}$

Thus the distance travelled when it decelerates = 56 - 40 = 16 m

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Hence option a(✔️) is the required distance.
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Hope this is ur required answer

Proud to help you