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Let v(t) = t^2 - 3t be the velocity, in feet per second, of an object at time t,

ID: 3142098 • Letter: L

Question

Let v(t) = t^2 - 3t be the velocity, in feet per second, of an object at time t, in seconds (a) What is the initial velocity? initial velocity = ____________ (include units help (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 = ______________ seconds (c) What is the meaning of the quantity v(4) Select all that apply if more than one statement is correct. The object's velocity in 4 seconds. The object's velocity in 4 hours. How much the object has moved in 4 seconds. The average velocity of the object over the 4 second interval. In how many seconds will the object have moved 4 ft. In how many hours will the velocity be 4 ft/sec. None of the above

Explanation / Answer

(a) We have the velocity function given by

v(t)=t2-3t

where velocity has the unit feet per second.

Now, initial velocity v0 is defined as the velocity when time is zero.

hence, substitute t=0 in v(t)

we get,

v0=(0)2-3*0

v0=0 feet per second

that is initial velocity is 0 ft/sec

(b) when the velocity of object is zero i.e. v=0,

t2-3t=0

t(t-3)=0

t=0 seconds, t=3 seconds

i.e velocity is zero when time is 0 seconds and 3 seconds.

(c) v(t) descibes object's velocity at time t that is velocity v is a function of time t.

Therefore v(4) tells about the object's velocity in 4 seconds.

Also velocity describes the rate of change of displacement of object that is, v(t) tells how much object moved in t seconds.

therefore v(4) tells that how much object moved in 4 seconds.

thus, option A. the object's velocity in 4 seconds.

and option C. How much object has moved in 4 seconds.

are both correct options