Apply the equation of motion relating the final velocity of an object to its initial velocity, uniform acceleration, and time (vf = vi + at) problems 5,6 63 5. A race car's forward velocity increases from Answer: 4.0 m/s to 36 m/s over a 4.0-s time interval. What is its average acceleration? 6. The race car in the previous problem slows from 36 m/s to 15 m/s over 3.0 s. What is its average acceleration? . . . Use appropriate significant figures to record answers from a mathematical operation, with 13 the correct number of digits problem & 8. Significant Figures Solve the following problems, using the correct number of signifi- Answer: cant figures each time. a. 10.8 g - 8.264 g . . . ... b. 4.75 m - 0.4168 m c. 139 cm x 2.3 cm d. 13.78 g / 11.3 ml e. 1.6 km + 1.62 m + 1200 cm ". . . . . . . ..Classify physical quantities into vector and scalar quantities (distance, mass, displacement, as mentioned in the book 34 speed, velocity, acceleration, force, work, energy, pressure) Vectors and Scalars Scalars Vectors As you might imagine, there are many kinds of measurements and numbers used to represent or describe motion. If you needed to describe how far you ran, you might say that you ran 1.6 km. If you needed to run to a specific location, you might say that you need to run 1.6 km north. Many quantities in physics have both size, also called magnitude, and direction. A quantity that has both magnitude and direction is called a vector. You can represent a vector with an arrow. The length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. A quantity that is just a number without any direction, such as distance, time, or temperature, is called a scalar. In this textbook, we will use boldface letters to represent vector quantities and regular letters to represent scalars. Apply the alternative equation of motion relating an object's final velocity to its initial velocity, its constant aceleration, problem 16 67 and its initial and final positions (v2f = v2i + 2a(xf - xi)) 16. A golf ball rolls up a hill toward a miniature-golf Answer: hole. Assume the direction toward the hole is positive. a. If the golf ball starts with a speed of 2.0 m/s and slows at a constant rate of 0.50 m/s', what is its velocity after 2.0 s? b. What is the golf ball's velocity if the constant . . . . . acceleration continues for 6.0 s? c. Describe the motion of the golf ball in words and with a motion diagram. Define a coordinate system and identify the origin, position, and distance in a coordinate figure 9 36 system10 Define and calculate the average acceleration problem 12 64 12. Position-Time and Velocity-Time Graphs Two joggers run at a constant velocity of Answer: 7.5 m/s east. Figure 10 shows the positions of both joggers at time t = 0. a. What would be the difference(s) in the position-time graphs of their motion? . .. . .... b. What would be the difference(s) in their velocity-time graphs? . . . . . .. . . . .... . . . ... East 15 m west Origin 15 m east Figure 10 12 Calculate the displacement as the area under the curve of a velocity-time graph problem 2 62 2. Use the v-t graph of the toy train in Figure 9 to answer these questions. 12.0 10.0 a. When is the train's speed constant? 8.0 b. During which time interval is the train's acceleration positive? $ 6.0 c. When is the train's acceleration most negative? 8 4.0 Velo 3. Refer to Figure 9 to find the average acceleration of the train during the 2.0 following time intervals. 0.0 10.0 20.0 30.0 40.0 a. 0.0 s to 5.0 s b. 15.0 s to 20.0 s c. 0.0 s to 40.0 s Figure 9 Time (s)