Question

A particle moves along the x-axis with its position at time t given by where a and b are constants and . For which of the following values of t is the particle at rest?

a) (t = a/2b)
b) (t = b/2a)
c) (t = a/b)
d) (t = b/a)

Answer 1

To determine when the particle is at rest, one must differentiate its position function with respect to time to find the velocity function and then identify the time at which this velocity is zero.

Step-by-step explanation:

The question asks at what value of time t is a particle at rest if its position is given by a function involving constants a and b. The particle is at rest when its velocity (the derivative of its position function) is zero. Without the specific position function, we cannot calculate the exact time, but in general terms, to find the time when the particle is at rest, we would differentiate the position function with respect to time to get the velocity function, then solve for t where the velocity equals zero.