Let v(t)=t^2−3t be the velocity, in feet per second, of an object at time t , in seconds.
(c) What is the meaning of the quantity v(4)? Select all that apply if more than one statement is correct.
A. In how many seconds will the object have moved 4 ft.
B. The object's velocity in 4 seconds.
C. The average velocity of the object over the 4 second interval.
D. In how many hours will the velocity be 4 ft/sec.
E. The object's velocity in 4 hours.
F. How much the object has moved in 4 seconds.
G. None of the above
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a b c
To find the meaning of the quantity v(4) for the given function v(t) = t^2 - 3t, we need to substitute t = 4 into the function.
v(4) = (4)^2 - 3(4)
= 16 - 12
= 4
Now let's analyze each option to see which statements are correct:
A. In how many seconds will the object have moved 4 ft. - This statement is not correct because v(4) represents the velocity of the object at 4 seconds, not the distance traveled.
B. The object's velocity in 4 seconds. - This statement is correct. v(4) represents the velocity of the object after 4 seconds.
C. The average velocity of the object over the 4-second interval. - This statement is not correct. v(4) only gives the instantaneous velocity at exactly 4 seconds, not the average velocity over an interval.
D. In how many hours will the velocity be 4 ft/sec. - This statement is not correct since v(4) is not equal to 4 ft/sec.
E. The object's velocity in 4 hours. - This statement is not correct. v(4) represents the velocity of the object at 4 seconds, not 4 hours.
F. How much the object has moved in 4 seconds. - This statement is not correct. v(4) represents the velocity, not the distance traveled.
G. None of the above - This option is not correct since option B is correct.
Therefore, the correct statement for the meaning of v(4) is B. The object's velocity in 4 seconds.