More Applications of Derivatives 197For which value(s) oft(t 1 ,t 2 ,t 3 ) is:(a) the particle moving to the left?
(b) the acceleration negative?
(c) the particle moving to the right and
slowing down?- The velocity function of a particle is shown
in Figure 9.6-3.
(^01)
1
–1
–2
–3
–4
–5
2
3
4
5
234
v(t)
v
t
Figure 9.6-3
(a) When does the particle reverse
direction?
(b) When is the acceleration 0?
(c) When is the speed the greatest?
- A ball is dropped from the top of a 640-foot
building. The position function of the ball
iss(t)=− 16 t^2 +640, wheretis measured in
seconds ands(t) is in feet. Find:
(a) The position of the ball after 4 seconds.
(b) The instantaneous velocity of the ball at
t=4.
(c) The average velocity for the first
4 seconds.
(d) When the ball will hit the ground.
(e) The speed of the ball when it hits the
ground.- The graph of the position function of a
moving particle is shown in Figure 9.6-4.
11
023423456 7s(t)s(seconds)(feet)tFigure 9.6-4(a) What is the particle’s position att=5?
(b) When is the particle moving to the left?
(c) When is the particle standing still?
(d) When does the particle have the
greatest speed?Part B Calculators are allowed.- The position function of a particle moving
on a line iss(t)=t^3 − 3 t^2 +1,t≥0, where
tis measured in seconds andsin meters.
Describe the motion of the particle. - Find the linear approximation of f(x)=
sinxatx=π. Use the equation to find
the approximate value of f
(
181 π
180)
.- Find the linear approximation of f(x)=
ln (1+x)atx=2. - Find the coordinates of each point on the
graph ofy^2 = 4 − 4 x^2 at which the tangent
line is vertical. Write an equation of each
vertical tangent. - Find the value(s) ofxat which the graphs
ofy=lnxandy=x^2 +3 have parallel
tangents. - The position functions of two moving
particles ares 1 (t)=lntands 2 (t)=sintand
the domain of both functions is 1≤t≤8.
Find the values oftsuch that the velocities
of the two particles are the same.