Final answer:
The question asks for the time elapsed between the maximum speed and maximum acceleration during the simple harmonic motion of an object. To find this, one must know the amplitude of the motion, but since it's not provided, the problem cannot be fully solved. The elapsed time would be a quarter of the period of the oscillation.
Step-by-step explanation:
The student's question involves an object performing simple harmonic motion (SHM) on a frictionless surface. To determine the time between when the object's speed is at a maximum and when its acceleration is at a maximum, we analyze the properties of SHM. An important characteristic of SHM is that these two instances are separated by a quarter of the period (T/4), as the maximum speed occurs at the equilibrium point, and the maximum acceleration occurs at the endpoints of the motion (the amplitude). During SHM, an object's speed v and acceleration a are related to the angular frequency ω through the equations v = ωX and a = ω^2X, where X is the amplitude. The angular frequency can be calculated from the maximum speed and acceleration using the equation ω = v/X = √(a/X).
Given the maximum speed (v = 1.25 m/s) and maximum acceleration (a = 6.89 m/s²), we can calculate the angular frequency (ω) and subsequently the period (T = 2π / ω). Once the period is known, the elapsed time is simply T/4. However, without the amplitude (X), it isn't possible to proceed with the calculation. Additional information regarding the amplitude is necessary to solve this problem completely.