Q85 / 150 · MHT CET 2019 (Shift 2) · Mathematics

A particle moves so that x = 2 +27t- $t^{3}$ . The direction of motion reverses after moving a distance of … units.

A
80
Correct answer
B
56
C
60
D
65

Solution

We have,

x = 2 + 27 t - t^{3}

\Rightarrow \frac{d x}{d t} = 27 - 3 t^{2}

Since, direction will be reverse,

∴ \frac{d x}{d t} = 0

\Rightarrow 27 - 3 t^{2} = 0

\Rightarrow t = 3

∴

Distance

x = 2 + 27 t - t^{3}

= 2 + 27 \times 3 - {(3)}^{3}

= 2 + 81 - 27 = 56

units

Hence, the correct answer is option: 'B'.

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