Using the graph below, find the acceleration of the object during the time interval from t = 3 seconds to t = 5 seconds. Velocity - m/sec 50- 40 30. 20 10. 0 0 1 -0.1 m/s² O-10 m/s² O-2 m/s² -0.5 m/s² 3 Seconds 2 4 5 6

As shown in Figure 2.9, Whipple chose a coordinate system that was different from Cralls. There are many possible coordinate systems that can be used to analyze the motion of the cart. For example, a third student (Yoon) chose to place the origin of her coordinate system at position A (the) carts initial position) and use a southward-pointing y axis as her positive axis. a. Use the distance information given in Table 2.2 to make a new table that gives the carts position at each of the 16 times according to Yoons coordinate system. Hint: A sketch similar to Figure 2.9 is a good place to start. b. Use the data in your table to make a new position-versus-time graph. Hint: CHECK and THINK about your graph by comparing it with Figure 2.6.

The kinematic equations can describe phenomena other than motion through space and time. Suppose x represents a persons bank account balance. The units of x would be dollars (), and velocity v would give the rate at which the balance changes (in units of, for example, /month). Acceleration would give the rate at which v changes. Suppose a person begins with ten thousand dollars in the bank. Initial money management, leads to no net change in the account balance so that v0 = 0. Unfortunately, management worsens over time so that a = 2.5 102 /month2. Assuming a is constant, find the amount of time in months until the bank account is empty

Tectonic plates are large segments of the Earth's crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?

Consider Concept Map 1,1, which provides an overview of motion. Review Sections 1,2 and 1,3 and make a list of at least five additional concepts you could add to the map. Now consider where to place these concepts on the map. Keep in mind that general, more inclusive concepts go towards the top, whereas more specific ideas and examples go toward the bottom. Place your concepts on the map. Draw the possible connections between your five new concepts and the rest of the map. Remember to use "linking words'' to create propositions and to express your ideas clearly. When you've finished updating your map, compare your revised concept map with that of a classmate's. Are they identical? Would you expect them to be?

Kinematics graphs are great for showing how a quantity depends on time. For example, an acceleration-versus-time graph shows how acceleration depends on time. a. Based on your experience with two other kinematics graphs (position- and velocity-versus-time), describe how to plot an acceleration-versus-time graph. b. Describe how all three kinematics graphs are connected by slopes of tangent lines (derivatives). c. If a particles acceleration is positive and constant, what is the shape of the curve in each of the three kinematics graphs?

A fireworks shell is accelerated from rest to a velocity of 65.0 m/s over a distance of 0.250 m. (a) How long did the acceleration last? (b) Calculate the acceleration.

Astronauts on a distant planet toss a rock into the air. With the aid of a camera that takes pictures at a steady rate, they record the rocks height as a function of time as given in the following table. (a) Find the rocks average velocity in the time interval between each measurement and the next. (b) Using these average velocities to approximate instantaneous velocities at the midpoints of the time intervals, make a graph of velocity as a function of time. (c) Does the rock move with constant acceleration? If so, plot a straight line of best fit on the graph and calculate its slope to find the acceleration.

An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration have the same sign on the way up as on the way down?

A student drives a moped along a straight road as described by the velocity-versus-time graph in Figure P2.12. Sketch this graph in the middle of a sheet of graph paper. (a) Directly above your graph, sketch a graph of the position versus time, aligning the time coordinates of the two graphs. (b) Sketch a graph of the acceleration versus time directly below the velocity-versus-time graph, again aligning the time coordinates. On each graph, show the numerical values of x and ax for all points of inflection. (c) What is the acceleration at t = 6.00 s? (d) Find the position (relative to the starting point) at t = 6.00 s. (e) What is the mopeds final position at t = 9.00 s? Figure P2.12