Question

The position $x$ of a particle with respect to time t along $x$ -axis is given by $x = 9t^2-t^3$ where $x$ is in metres and $t$ in seconds. What will be the position of this particle when it achieves maximum speed along the $+x$ direction?

• A. 54 m
• B. 81 m
• C. 24 m
• D. 32 m

Answer 1

The Correct Option is A

 To find the position of the particle when it achieves maximum speed along the \(+x\) direction, we must first determine the expression for the velocity of the particle and then find when this velocity is maximized.

1. Find the velocity function. The velocity \(v(t)\) is the derivative of the position function \(x(t)\) with respect to time \(t\).
2. Determine when velocity is maximum. To find the maximum velocity, take the derivative of \(v(t)\) with respect to \(t\) and set it equal to zero.
3. Find the position at maximum velocity. Substitute \(t = 3\) back into the position function \(x(t)\) to find the position of the particle at this time.

Therefore, the position of the particle when it achieves maximum speed along the \(+x\) direction is 54 meters.