When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally. Students will often only choose the first option as an accelerating vehicle. They think of the others as decelerating and constant velocity.
Have students analyze the equation before providing the answer to the units. Stress that m/s 2 are a short way of saying (m/s)/s. It is a good idea to keep saying (m/s)/s in order to emphasize the fact that acceleration is the change in velocity (m/s) over a period of time (s).
For problems, it is a good idea to go through the steps on the overhead projector or board so students can see the process instead of just seeing the solution. Allow them some time to work on problems and then show them the proper solutions. Do not rush through the solutions. Discuss the importance of units at every step. Problem solving is a developed skill and good examples are very helpful.
To make the situations more concrete, use an automobile as an example. For example, the first combination would be a car moving to the right (v is +) and accelerating to the right (a is +), so the speed will increase. Some students may be confused by the latter two examples, thinking that a negative acceleration corresponds to slowing down and a positive acceleration corresponds to speeding up. Emphasize that the directions of velocity and acceleration must both be taken into account. In the third example, the velocity and acceleration are in the same direction, so the object is speeding up. In the fourth case, they are in opposite directions, so the object is slowing down.
The equation for v avg is only valid if the velocity increases uniformly (a straight line in a velocity-time graph) or, in other words, if the acceleration is constant.
Students may think “B” is at rest and “C” is moving backwards or to the left. If so, they are confusing position-time graphs with velocity-time graphs. Ask them to look at “B” and think about what it means if velocity stays the same or look at “C” and ask them what it means if velocity is decreasing. A good exercise for the students at this time would be the use of the Phet web site: http://phet-web.colorado.edu/web-pages/index.html NOTE: These simulations are downloadable so you can avoid the need for internet access after a onetime download. If you choose the “Motion” simulations and then choose the “Moving man” option, the students can observe the motion of a man (constant velocity, speeding up, slowing down, at rest) and see the graphs of position-time, velocity-time and acceleration-time. You might start with “at rest” and ask them to predict the shape of each graph before running the simulation. Then ask them how each would change if he moved forward with a constant speed. Follow this with other changes, such as changing the starting position or accelerating the walker.
Equations (1) and (2) are the definitions of velocity and acceleration. Equations (3), (4), and (5) are only valid for uniform acceleration. Show students how to derive equation (4) by combining (1), (2), and (3). Then allow students some time to derive (5) from (1), (2), and (3) by eliminating time. Since (4) and (5) are derived from the first three, there are no problems that can be solved with them that could not have been solved by using the first three equations. It might be easier to use (4) and (5) but it is not necessary. They do not represent any “new” rules.
For problems, it is a good idea to go through the steps on the overhead projector or board so students can see the process instead of just seeing the solution. Allow them some time to work on problems and then show them the proper solutions. Do not rush through the solutions. Discuss the importance of units at every step. Problem solving is a developed skill and good examples are very helpful. After using equation (4) to solve the first problem, show the students that they would obtain the same answer by using equation (3) followed by equation (1). Similarly, the second problem can be solved with equation (5) or by using (3), then (1), then (2).
The car is accelerating in each example except for the cruise control. The first is positive acceleration, the second is negative acceleration, and the fourth is accelerating because direction is changing (and thus velocity is changing, even though speed is constant). Centripetal acceleration will be covered in a later chapter but it is good to introduce the idea here, so students realize that acceleration is any change in velocity (either a change in the magnitude of velocity, or a change in the direction of velocity, or both).