When a 1984 Alfa Romeo Spider sports car accelerates at the maximum possible rate, its motion during the first 20 s is extremely well modeled by the simple equation v x 2 = 2 P m t where P = 3.6 × 10 4 watts is the car’s power output, m = 1200 kg is its mass, and v x is in m/s. That is, the square of the car’s velocity increases linearly with time. a. Find an algebraic expression in terms of P, m, and t for the car’s acceleration at time t. b. What is the car’s speed at t = 2 s and t = 10 s? c. Evaluate the acceleration at t = 2 s and t = 10 s.
When a 1984 Alfa Romeo Spider sports car accelerates at the maximum possible rate, its motion during the first 20 s is extremely well modeled by the simple equation v x 2 = 2 P m t where P = 3.6 × 10 4 watts is the car’s power output, m = 1200 kg is its mass, and v x is in m/s. That is, the square of the car’s velocity increases linearly with time. a. Find an algebraic expression in terms of P, m, and t for the car’s acceleration at time t. b. What is the car’s speed at t = 2 s and t = 10 s? c. Evaluate the acceleration at t = 2 s and t = 10 s.
When a 1984 Alfa Romeo Spider sports car accelerates at the maximum possible rate, its motion during the first 20 s is extremely well modeled by the simple equation
v
x
2
=
2
P
m
t
where
P
=
3.6
×
10
4
watts is the car’s power output, m = 1200 kg is its mass, and vxis in m/s. That is, the square of the car’s velocity increases linearly with time.
a. Find an algebraic expression in terms of P, m, and t for the car’s acceleration at time t.
b. What is the car’s speed at t = 2 s and t = 10 s?
c. Evaluate the acceleration at t = 2 s and t = 10 s.
(d) Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.)
x
=
y
=
(e) How long after being released does the stone strike the beach below the cliff?s (f) With what speed and angle of impact does the stone land?
vf
=
m/s
?
=
° below the horizontal
d. What is the mass of 3 L of water?
e. How many seconds are in one day?
f. What is the density in grams per cubic centimeter of a rock that has a mass of 1 kg and a volume of 280 cm?
c) It's one thing to say "use the initial velocity to find the range," and another thing to actually measure the initial velocity (fyi, there were no radar guns in the 1600s). One method of finding the initial velocity (I encourage you to think about how you might figure this out before reading what I wrote) might be as follows: Take the cannon to the test-fire range, and measure out several, equal masses of gunpowder. •Set the cannon to a typical firing angle, say 5°. •Fire the cannon multiple times, measuring the range of each shot. Since conditions will vary •slightly from one shot to another, the range will vary too. Assuming no major changes in firing conditions, all shots should land in the same area, approximately. If the average range of the test shots was 1480 m, what is the initial velocity for this cannon? d) Now that you know the initial velocity of the cannon, find the equation the artillery crew will use to calculate the appropriate firing angle for a target at a given…
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