) 1/2 (Raising to the power of 1/2 is the same operation as square root)

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1 Physics 1110 Written Homework 1: Motion in 1D Due: Sept 3 or 4 in your recitation section NAME Lab/Recit Day: Wed Thurs Lab/Recit Time: 8am, 9am, 10am, 11am, 12pm, 1pm, 2pm, 3pm, 4pm TA Name: In this assignment and all those that follow, be sure to present your reasoning (or show your work) when the question asks or you will not receive any credit. Print the assignment out, do your work on the print out, and hand it in at the beginning of your recitation section on the date indicated above. PART 1. This part of the assignment involves determining the dimensions of various formulas in which we will only be concerned with the dimensions of length [L] and time [T]. Pure numbers (e.g,. 2) or symbols that represent a number (e.g., π) are dimensionless. As shown in the figure, a right circular cone has a height h, a base with a radius of r, and a side length s. All three of these quantities (h,r,s) have dimensions of length [L]. 1. Determine the overall dimensions of each of the following formulas. Example: If the formula is π 3 r 2 h. Solution: Dimensions are [L]2 * [L] which is [L] 3 i) πr 2 + πrs ii) ( r 2 + h 2 ) 1/2 (Raising to the power of 1/2 is the same operation as square root) iii) πr 2 + 4πrs 2. Considering only dimensions, what s wrong with the following equation: r 2 = h hs2? Briefly explain your reasoning. 1

2 3. For time, displacement, velocity, and acceleration the overall dimensions are as follows: t =====> [T ] d =====> [L] v =====> [L] [T ] a =====> [L] [T ] 2 For each of the following equations of motion, analyze the dimensions of each term in the equations. Note that the subscripts only indicate a difference between initial velocity and final velocity; both are still just velocities in terms of dimensions. Please show your work. Example: Solution: v = v 0 + at v v 0 a t [L] [T ] = [L] [T ] + [L] [L] [T ] (which is again 2 [T ] [T ] ) (So the dimensions agree, as they must for a valid equation!) i) d = v 0 t + 1 at 2 2 ii) v 2 = v a d PART 2. In this part of the assignment, consider a unicyclist riding along a sidewalk. When he comes to a bump he decides to back up immediately and retrace his motion backward. He completes this maneuver in 3 seconds. His position and velocity at half-second intervals are given by the data shown in the following table. Note that SI units are used for all quantities. Also note that he is initially moving in the x direction. Time t (s) Position x (m) Velocity v (m/s)

3 4. Use the graph paper at the end of the assignment to make separate graphs of the unicyclist s position and velocity versus time. Graph the points and draw a continuous, smooth line through them. Note: In this first assignment the axes are presented for your graphs. In future assignments you will be expected to draw them yourself. A complete graph must include neatly labeled axes including units (e.g., x (m), t (sec), v (m/s)), clear tic marks on the axes with the values marked neatly (e.g, 0.5, 1.0, 1.5, etc), and a graph title (e.g., Position vs Time). 5. What is the unicyclist s total displacement? Show your work. (a) 1.35 m (b) m (c) m (d) 2.70 m (e) 0.00 m 6. What is the total distance that the unicyclist traveled? Show your work. (a) 1.35 m (b) m (c) m (d) 2.70 m (e3) 0.00 m 7. What is the value of his average velocity? Present your reasoning. (a) -1.8 m/s (b) -0.9 m/s (c) 0.0 m/s (d) 0.9 m/s (e) 1.8 m/s 8. What is the value of his average speed? Present your reasoning. (a) -1.8 m/s (b) -0.9 m/s (c) 0.0 m/s (d) 0.9 m/s (e) 1.8 m/s 3

4 9. What is his acceleration from t = 1.0 s to t = 2.0 s? Present your reasoning. (a) -1.2 m/s 2 (b) -0.6 m/s 2 (c) 0.0 m/s 2 (d) 0.6 m/s 2 (e) 1.2 m/s As the unicyclist moves how does his acceleration vary? (a) Acceleration starts positive, goes to zero, and becomes negative. (b) Acceleration starts negative, goes to zero, and becomes positive. (c) Acceleration starts positive and remains positive throughout his motion. (d) Acceleration starts negative and remains negative throughout his motion. (e) Acceleration is zero throughout his motion. 11. Which of the following graphs best represents the unicyclist s acceleration versus time? 12. Which of the following is evidence that his acceleration is constant (that is, not changing)? (a) The displacement x is always nonnegative. (b) The velocity is always increasing. (c) The velocity becomes zero at t = 1.5 s. (d) Equal intervals of time correspond to equal intervals of velocity. 4

5 13. (Tougher One) Now abstract yourself from the numerical values given in the table above. Consider the motion of the unicyclist after he stops at the bump and begins to move in the +x direction with a constant positive acceleration a. How long will it take him to travel a distance of x meters? Present your reasoning. (a) x a (b) a 2x (c) 2x a (d) x a (e) 2x a 5

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