Palmer 9/22/21 03 APC Practice Problems 01 - Introductory Concepts and 1D Motion - Solutions.docx 1 of 8

FOS4 – Practice Problems – Introductory Concepts and 1D Motion – APC

1) The standard kilogram is a platinum-iridium cylinder 39.0 mm in height and 39.0 mm in diameter. What is the density of the material in kg/m3?

2) What is the mass of a material with density ρ is required to make a hollow spherical shell having inner radius r1 and outer radius r2?

3) Two spheres are cut from a certain uniform rock. One has a radius 4.50 cm. The mass of the other is exactly five times greater. Find its radius.

4) Suppose your hair grows at the rate 1/32 in. per day. Find the rate at which it grows in nanometers per second.

5) An auditorium measures 40.0 m x 20.0 m x 12.0 m. The density of air is 1.20 kg/m3. What are (a) the volume of the rum in cubic feet and (b) the weight of the air in the room in pounds?

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6) A section of land has an area of 1.00 square mile and contains 640 acres. Determine the number of square meters in 1.00 acre.

I apologize for the effrontery of the sig fig issues in my answer. Feel free to cry sad tears. 7) One gallon of paint (volume = 3.78 x 10-3 m3) covers an area of 25.0 m2. What is the thickness of the paint on the wall?

8) A hydrogen atom has a diameter of approximately 1.06 x 10-10 m, as defined by the diameter of the spherical electron cloud around the nucleus. The hydrogen nucleus has.a diameter of approximately 2.40 x 10-15 m. (a) For a scale model, represent the diameter of the hydrogen atom by the length of an American football field (100 yd = 300 ft), and determine the diameter of the nucleus in millimeters. (b) The atom is how many times larger in volume than its nucleus?

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9) The position versus time for a certain particle moving along the x axis is shown. Find the average velocity in the time intervals (a) 0 to 2 s, (b) 0 to 4 s, (c) 2 s to 4 s, (d) 4 s to 7 s, (e) 0 to 8 s.

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10) A position-time graph for a particle moving along the x axis is shown. (a) Find the average velocity in the time interval t = 1.50 s to t = 4.00 s. (b) Determine the instantaneous velocity at 2.00 s by measuring the slope of the tangent line shown in the graph. (c) At what value of t is the velocity zero?

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11) A particle starts from rest and accelerates as shown in the figure. Determine (a) the particle’s speed at t = 10.0 s and at t = 20.0 s, and (b) the distance traveled in the first 20.0 s.

12) A particle moves along the x axis according to the equation x = 2.00 + 3.00t -1.00t2, where x is in meters and t is in seconds. At t = 3.00 s, find (a) the position of the particle, (b) its velocity, and (c) its acceleration. 2-15) ; ; ; ;

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Note: The acceleration is independent of time & that it is Uniformly Acceleration Motion Also note: This problem uses the power rule to take the derivative of the function. The power rule works like this:

The derivative of as a function of t is equal to

Also also note: The derivative of a constant with respect to time is zero. That is because the derivative with respect to time is the “time rate of change” of a function. If that function is not changing as a function of time, then the derivative is zero. 13) An object moves along the x axis according to the equation x(t) = (3.00t2 – 2.00t + 3.00) m. Determine (a) the average speed between t = 2.00 s and t = 3.00s, (b) the instantaneous speed at t = 2.00 s and t = 3.00 s, (c) the average acceleration between t = 2.00 s and t = 3.00 s, and (d) the instantaneous acceleration at t = 2.00 s and t = 3.00 s. 2-16)

a) &

b) Instantaneous speed (or instantaneous velocity with out the direction) is simply the derivative of position as a function of time or

& (these are the instantaneous speeds at t = 2 &

t = 3 seconds.)

c)

d) (please note (again) that this is Uniformly Accelerated

Motion.) 14) An object moving with uniform acceleration has a velocity of 12.0 cm/s in the positive x direction when its x coordinate is 3.00 cm. If its x coordinate 2.00 s later is -5.00cm, what is its acceleration?

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15) A particle moves along the x axis. Its position is given by the equation x = 2.00 + 3.00t – 4.00t2 with x in meters and t in seconds. Determine (a) its position when its position changes direction and (b) its velocity when it returns to the position it had at t = 0. 2-25) (a)The particle will change direction when the velocity is equal to zero. In other words, you need to stop in order to change directions. We need to figure out the velocity. Velocity is the derivative of position with respect to time.

(b) at t = 0, so

16) Speedy Sue, driving at 30.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 155 m ahead traveling at 5.00 m/s. Sue applies her brakes but can accelerate only at -2.00 m/s2 because the road is wet. Will there be a collision? If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of closest approach between Sue’s car and the van.

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