Week 1 Practice Problems PDF

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Week 1 Practice...

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Physics 131 Practice Problems Week 1 Problem 1: Filling a swimming pool How many liters (L) of water does it take to fill a swimming pool that is 15.0 feet long, 15.0 feet wide, and 8.0 feet deep? The volume of the swimming can be computed using 𝑉 = 𝑙 × 𝑤 × ℎ, and you will also need to convert units. Useful conversion: 1-ft = 0.3048-m, 1-L = 1000-cm!.

Problem 2: Interpreting a velocity vs time graph The motion of a particle is described in the velocity vs. time graph shown to the right. A. Find the displacement of the particle during the time interval 2 £ t £ 7 s.

B. Find the average velocity of the particle during the time interval 2 £ t £ 7 s.

C. During which portions of the motion is the speed of the particle: a. Increasing? b. Remaining constant? c. Decreasing?

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D. During which portions of the motion is the acceleration of the particle: a. Positive? b. Zero? c. Negative? E. In the space below, sketch an acceleration versus time graph for this motion.

F. Do your answers to part D agree with your sketch above? If not, resolve any inconsistencies.

Problem 3: Determining displacement from acceleration A car is moving with a constant acceleration. At t = 5.0 s its velocity is 8.0 m/s and at t = 8.0 s its velocity is 12.0 m/s. What is the displacement of the car in that interval of time?

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Problem 4: Free fall A ball is thrown vertically upwards with an initial velocity of 10 m/s, from a platform that is at a height of 75 m above the ground. The ball reaches a maximum height and, on the way down, misses the platform and falls all the way to the ground. Take the magnitude of the acceleration due to gravity to be 10 m/s2. A. What is the velocity of the ball just before it reaches the ground?

B. How many seconds is the ball in flight?

C. What is the maximum height above ground reached by the ball?

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Problem 5: Acceleration versus changing speed. For an object moving in one dimension, a positive velocity indicates that the object is moving in the positive direction and a negative velocity indicates that the object is moving in the negative direction. Below we will illustrate what we mean by positive and negative acceleration in the context of one-dimensional motion. Recall that acceleration is defined as the rate of change of velocity. We will use the usual coordinate system in which the +𝑥 -direction is to the right and the −𝑥 -direction is to the left A. For an object that moves along the 𝑥 -axis with constant acceleration, sketch a velocity versus time graph for the following four situations: 1) An object is moving in the positive 𝑥 -direction and its speed is increasing 2) An object is moving in the positive 𝑥 -direction and its speed is decreasing 3) An object is moving in the negative 𝑥-direction and its speed is increasing 4) An object is moving in the negative 𝑥-direction and its speed is decreasing 1)

2)

3)

4)

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B. For each of the graphs above, indicate whether the acceleration is in the positive 𝑥 direction or in the negative 𝑥 -direction. Recall that the acceleration is given by the slope on a velocity versus time graph, so a positive slope implies that the acceleration is in the positive 𝑥 -direction. Case 1: Case 2: Case 3: Case 4: C. In which of the above scenarios is the speed of the object increasing and yet it has a negative acceleration?

D. In which of the above scenarios is the speed of the object decreasing and yet it has a positive acceleration?

Problem 6: Interpreting position versus time graphs with non-constant acceleration The graph to the right shows the position versus time plot for a jogger. Again, use the usual coordinate convention ( +𝑥 to the right). A. In what direction (right or left) was the person jogging in the first 2 seconds?

B. In what time interval(s) was the jogger at rest?

C. At what instant in time did the jogger change directions?

D. What was the total distance that she jogged between 0 and 6 seconds?

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E. What was her net displacement in that time interval?

F. What was her average velocity between 0 and 6 seconds?

G. What was her instantaneous velocity at 𝑡 = 2-s? To compute the instantaneous velocity, draw a line that is tangent to the position versus velocity graph at 𝑡 = 2-s and then determine the slope of that tangent line, using any two convenient points on that line.

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