Question

Marked out of 1 Flag question A particle initially at origin moves along x-axis according to the rule dx/dt = x + 6.The time taken by the particle to transvers a distance of 96 units is Select one: O2ln(51) O ln (5) o 2logs o logs.

Answer 1

Given:

`(dx)/(dt)=x+6`

Let's find the time taken to transverse a distance of 96 units.

To find the distance, we have:

`\int_0^(96)(dx)/(x+6)`

Solving the integral, we have:

`\begin{gathered} [ln(x+6)]_0^(96)=t \\ \\ \\ [ln(96+6)-ln(6))=t \\ \\ =ln(102)-ln(6)=t \\ \\ =(ln(102))/(ln(6)) \\ \\ =ln((51)/(3)) \\ \\ =ln(17) \end{gathered}`

ANSWER:

`\begin{gathered} ln((51)/(3)) \\ \\ OR \\ \\ ln(17) \end{gathered}`