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
well, we are told that v(t) is the velocity at time t.
Looks like B to me.
Well, let's break it down!
A. In how many seconds will the object have moved 4 ft. - Not quite. V(4) represents velocity, not position.
B. The object's velocity in 4 seconds. - Yes! This is correct. v(4) gives us the velocity of the object at time t = 4 seconds.
C. The average velocity of the object over the 4 second interval. - Close, but no cigar. v(4) only gives the instantaneous velocity at t = 4 seconds, not the average over a 4-second interval.
D. In how many hours will the velocity be 4 ft/sec. - Nope! v(4) gives the velocity at 4 seconds, not the time it takes for the velocity to be 4 ft/sec.
E. The object's velocity in 4 hours. - Definitely not! v(4) represents the velocity at 4 seconds, not 4 hours.
F. How much the object has moved in 4 seconds. - Nope! v(4) only gives the velocity, not the position.
G. None of the above - Ding Ding Ding! You got it! The answer is G. None of the above.
Remember, velocity is all about how fast an object is moving, not where it is.
The correct answers are:
B. The object's velocity in 4 seconds.
C. The average velocity of the object over the 4 second interval.
F. How much the object has moved in 4 seconds.
So, v(4) represents the object's velocity at 4 seconds, the average velocity over the 4 second interval, and the distance the object has moved in 4 seconds.
To find the meaning of the quantity v(4), we need to substitute t = 4 into the given velocity function v(t) = t^2 - 3t.
So, v(4) = (4)^2 - 3(4) = 16 - 12 = 4 feet per second.
Now, let's determine the applicable statements:
A. In how many seconds will the object have moved 4 ft. - This statement is not applicable because v(4) represents the velocity at t = 4, not the position or displacement.
B. The object's velocity in 4 seconds. - This statement is correct since v(4) represents the velocity of the object at t = 4 seconds.
C. The average velocity of the object over the 4-second interval. - This statement is not applicable since v(4) is the instantaneous velocity at t = 4, not the average velocity over a time interval.
D. In how many hours will the velocity be 4 ft/sec. - This statement is not applicable since we are given the velocity at t = 4, not the time when the velocity is equal to 4 ft/sec.
E. The object's velocity in 4 hours. - This statement is not applicable because v(4) represents the velocity at 4 seconds, not 4 hours.
F. How much the object has moved in 4 seconds. - This statement is not applicable because v(4) represents the velocity, not the displacement or distance traveled.
G. None of the above - This statement is not correct since statement B is correct.
Therefore, the correct answer is B. The object's velocity in 4 seconds.