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:

$\frac{dx}{dt}=x+6$

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

To find the distance, we have:

$\int_0^{96}\frac{dx}{x+6}$

Solving the integral, we have:

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

ANSWER:

$\begin{gathered} ln(\frac{51}{3}) \\ \\ OR \\ \\ ln(17) \end{gathered}$