Final answer:
To find the velocity when the position is 16 m, we need to find the equation of motion using the acceleration function and integrate it to get the velocity function. By substituting the position value into the velocity function, we can calculate the velocity and determine the time taken.
Step-by-step explanation:
To determine the velocity of the particle when the position is 16 m, we need to find the time taken to reach this position. We can start by finding the equation of motion using the acceleration function given: a = √s m/s². By integrating the acceleration function, we can find the velocity function as: v = √(2s+c), where c is a constant.
Since the velocity is 0 m/s when t = 0, we can substitute these values into the equation to find c. Therefore, when s = 16 m, we can substitute it into the velocity function to find the velocity of the particle at that position and calculate the time taken.
The acceleration of a particle moving along a straight line is given by a = √ s m/s², where s is the displacement in meters. To determine the velocity when s = 16 m, we can integrate the acceleration with respect to s, since a = dv/dt and dv = a ds for constant acceleration. Considering the initial conditions of s = 0 and v = 0 when t = 0, the integrated velocity function would give us the velocity at s = 16 m. To find the time it takes to reach s = 16 m, we can further integrate the velocity function with respect to time or solve the kinematic equations with the given initial conditions and acceleration function.