Question

Question 12: a) What is the meaning of the average velocity, say between to O second to t - 1 second? Does it precisely describe the velocity as a function of time for the bowling ball's motion? Why or why not? b) What is the meaning of the average acceleration, say between t -1 second to t2 2 second? Does it precisely describe the velocity as a function of time for the bowling ball's motion? Why or why not? Question 13: As you may realize in Question 12, average velocity and acceleration can't precisely tell us accurate information about the bowling ball's motion at each single instant of time. Then do you have any idea about how to improve the concepts of average velocity and acceleration so that they may describe a motion more precisely? more precisely describe a motion, we can choose the time interval smaller and smaller, Question 14: To such as from l second, to ½ second, ¼ second, 1/8 second, l / 16 second. This means to have approach to zero, and then we can have instantaneous velocity and acceleration! at Aš dš Instantaneus Velocity lim Instantaneus Acceleration limã Then for an one-dimensional motion, we can write those equations in algebraic format, instead of vector format. For example, if we have a 1-D motion with a constant acceleration like the bowling ball's motion given initial position s, and initial (instantaneous) velocity viat t-0 and final position se and final (instantaneous) vr at time t, could you please drive equations of vr and sr using the given info?

Answer 1

Problem-12

part-a

Average Velocity :- It is defined as the ratio of distance travelled to the time taken.

$avg. V = \frac{x_2-x_1}{t_2-t_1} = \frac{\Delta x}{\Delta t}$

Therefore from t=0 to t=1 seconds the meaning of average velocity is that the distance travelled by the object during this 1 second is known as average velocity of the object in this time interval.

This does not describe velocity as function of time because this does not given us the instantaneous velocity at a particular time.

Part-b

Average acceleration:- Velocity over time elapsed

$avg. a = \frac{v_2-v_1}{t_2-t_1} = \frac{\Delta v}{\Delta t}$

Therefore from t=2 to t=2 seconds the meaning of average acceleration is that the increase of the velocity of the object during this 1 second is known as average acceleration of the object in this time interval.

This does not describe acceleration as function of time because this does not given us the instantaneous acceleration at a particular time.