Question

A particle moves so that x = 2 + 27t - t³. The direction of motion reverses after moving a distance of ______ units.

Options

• 80

• 56

• 60

• 65

Answer 1

A particle moves so that x = 2 + 27t - t³. The direction of motion reverses after moving a distance of 56 units.

Explanation:

We have, x = 2 + 27t - t³ 

`=> "dx"/"dy" = 27 - 3"t"^2`

Since, direction will be reverse,

`therefore "dx"/"dt" = 0`

⇒ 27 - 3t² = 0

⇒ t = 3

∴ Distance x = 2 + 27t - t³ 

= 2 + 27 × 3 - (3)³

= 2 + 81 - 27

= 56 units