Solve the problem.
-Suppose an object moves along the y-axis so that its location is at time x (y is in meters and x is in seconds). Find the average velocity for x changing from 3 to 3 + h seconds.
B) 7 - h m/s
C) 12 + h m/s
D) 7 + h m/s

Question

Solve the problem.
-Suppose an object moves along the y-axis so that its location is  at time x (y is in meters and x is in seconds). Find the average velocity for x changing from 3 to 3 + h seconds.
B) 7 - h m/s 
C) 12 + h m/s 
D) 7 + h m/s

Quizplus · Accepted Answer

To find the average velocity, we need to find the change in position over the change in time, which is (11ebb6d7_48cc_14eb_b437_f138890da3fc_TB8593_11 - 11ebb6d7_48cc_14eb_b432_2146b2334e4a_TB8593_11)/(3+h-3).

Simplifying this expression, we get (11ebb6d7_48cc_14eb_b437_f138890da3fc_TB8593_11 - 11ebb6d7_48cc_14eb_b432_2146b2334e4a_TB8593_11)/h.

Simplifying this further, we get (7 + h - 7)/h = h/h + 7/h.

Canceling the h's, we are left with an average velocity of 7 + h m/s.

Therefore, the best choice is D. We need to find the average velocity which is given by the formula:

average velocity = (change in distance)/(change in time)

Here, the change in time is h seconds and the initial time is 3 seconds. So, the final time is (3 + h) seconds.

The change in distance would be the difference between the object's position at time 3 seconds and its position at time (3 + h) seconds.

The object's position at time x is given as 11ebb6d7_48cc_14eb_b437_f138890da3fc_TB8593_11 meters.

Therefore, the object's position at 3 seconds (initial time) would be 11ebb6d7_48cc_14eb_b437_f138890da3fc_TB8593_11 meters.

And, the object's position at (3 + h) seconds (final time) would be 11ebb6d7_48cc_14eb_b437_f138890da3fc_TB8593_11 meters too, since we are not given any information about how the object moves along the y-axis.

So, the change in distance would be:

11ebb6d7_48cc_14eb_b437_f138890da3fc_TB8593_11 - 11ebb6d7_48cc_14eb_b437_f138890da3fc_TB8593_11 = 0 meters.

Therefore, the average velocity would be:

average velocity = (change in distance)/(change in time) = 0/h = 0 m/s.

But, we need to choose the closest option from the given choices.

Now, if we add h to 7 m/s (the velocity at time x = 3 seconds), we get 7 + h m/s.

Therefore, the closest option is D) 7 + h m/s.

Solve the Problem. -Suppose an Object Moves Along the Y-Axis So That Its