Question

A ball is thrown upward at time t=9 s on planet ubuntu, and its acceleration from time t=9 s to t=13 s is given by the function a(t)=4/(t−8) m/s² . use 4 time intervals of equal length to overestimate, and then underestimate, the relative velocity of the rising ball from time t=9 s to t=13 s.

Answer 1

To overestimate the relative velocity, assume constant acceleration and integrate. To underestimate, assume zero acceleration and sum velocities.

Step-by-step explanation:

To overestimate the relative velocity of the rising ball, we can assume that the acceleration is constant for each time interval. Since the ball is thrown upward, the acceleration is negative. Using the given function a(t) = 4/(t−8) m/s², we can calculate the acceleration at each time interval by substituting the values (9, 9.25, 9.5, 9.75) into the function. Using the calculated accelerations, we can then integrate to find the overestimated relative velocity.

To underestimate the relative velocity, we can assume that the acceleration is zero for each time interval. This means that the ball maintains a constant velocity during each interval. Using the same time intervals as before, we can calculate the velocities at each interval and sum them to find the underestimated relative velocity.