Let v(t) = t^2-2t be the velocity, in feet per second, of an object at time t, in seconds.?

Question

Let v(t) = t^2-2t be the velocity, in feet per second, of an object at time t, in seconds.

(a) What is the initial velocity?
initial velocity =
answer in units
(b) When does the object have a velocity of zero? If there is more than time, list all answers in a comma separated list.
t =

(c) What is the meaning of the quantity v(4) ? Select all that apply if more than one statement is correct.

A. In how seconds will the object have moved 4 ft.
B. How much the object has moved in 4 seconds.
C. The average velocity of the object over the 4 second interval.
D. The object's velocity in 4 hours.
E. In how many hours will the velocity be 4 ft/sec.
F. The object's velocity in 4 seconds.
G. None of the above

Answer 1

a)

v(0) = 0 ft/sec

b)

t^2-2t=0

t(t-2)=0

t=0; t=2

The object has velocity 0 when t=0 sec and t= 2 sec



c)

F.

Answer 2

Ans:

Answer 3

v(t) =t² - 2t



a) Initial Velocity = v(0) = 0 (in any units you care to choose. Light years per millisecond if you so choose. Zero is zero in any system of units. However non-zero values are only valid for input units of seconds and the output is in feet per second.)



b) v(t) = 0 = t² - 2t = t(t-2)

The velocity is 0 at.

t = 0

t = 2 seconds



c) v(4) = the velocity at t = 4 seconds. Choice F

Answer 4

Let v(t) = t^2-2t be the velocity, in feet per second, of an object at time t, in seconds.



(a) What is the initial velocity?

initial velocity = 0 since t = 0 and no initial velocity Vo is in the formula



(b) When does the object have a velocity of zero? If there is more than time, list all answers in a comma separated list.

if t1= 0, both t1^2 and 2t1 are 0, therefore V = 0

furthermore if V = 0 , then t2^2 = 2t2 ....and t2 = 2 sec

This means that in the range of time 0÷2 sec velocity V is negative (2t > t^2), @ t = 2 sec velocity V = 0 and from then on it becomes positive





(c) What is the meaning of the quantity v(4) ? Select all that apply if more than one statement is correct.

A. In how seconds will the object have moved 4 ft.

B. How much the object has moved in 4 seconds.

C. The average velocity of the object over the 4 second interval.

D. The object's velocity in 4 hours.

E. In how many hours will the velocity be 4 ft/sec.

F. The object's velocity in 4 seconds.

G. None of the above



F. The object's velocity in 4 seconds is the right answer