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Objective: To identify whether positive, negative, or zero work is being done, to identify the force that is doing the work, and to describe the energy transformation associated with such work.

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Velocity-Time Graphs

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Formulate general ideas regarding v-t graphs that contrast constant vs. changing speeds and motions in the + vs. the - directions.

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Formulate general ideas regarding v-t graphs that are associated with different types of speed changes and with direction changes.

There are patterns in velocity-time graphs. It’s your turn to find them.

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Put it all together to explain how a multi-stage motion is associated with a complex v-t graph.

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Formulate general ideas regarding v-t graphs that contrast moving fast vs. moving slow and speeding up vs. slowing down.

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Velocity versus Time Graphs Velocity refers to how fast an object is moving (known as speed) AND in what direction. A plus (+) or minus (-) sign is often used to indicate direction. An object with a velocity of -34 m/s is moving with a speed of 34 m/s in the - direction. A group of students are investigating how velocity vs. time graphs can be used to describe motion. Using a motion detector, they move in a variety of ways and observe the corresponding plots of velocity vs. time on a computer monitor. Experiment 1: The students move away from the detector in three separate trials. In trial 1, they move slowly at a constant speed. In trial 2, they move fast at a constant speed. In trial 3, they continually change their speed from slow (initially) to fast (finally). The plots for the three trials are shown in Figure 1. Experiment 2: The students conduct two constant speed trials. In trial 4, they move towards the detector slowly. In trial 5, they move towards the detector, but with a faster speed than in trial 4. The plots for the two trials are shown in Figure 2. Experiment 3: The students conduct three changing speed trials. In trial 6, they walk away from the detector from fast to slow. In trial 7, they walk towards the detector from fast to slow. In trial 8, they walk towards the detector from slow to fast. The plots for the three trials are shown in Figure 3. Experiment 4: The students constructed a ramp and rolled a cart along the ramp. The cart was given a push from the bottom of the ramp. The cart decreased its speed as it rolled up the ramp, it turned around, and it increased its speed as it rolled down the ramp. They performed Trial 9 with the motion detector at the top of the ramp. In trial 10, the motion detector was at the bottom of the ramp. See Figure 4.

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Stopping Distance One aspect of safe driving involves the ability to stop a car readily. This ability depends upon the driver's alertness and readiness to stop, the conditions of the road, the speed of the car, and the braking characteristics of the car. The actual distance it takes to stop a car consists of two parts - the reaction distance and braking distance. When a driver sees an event in his/her field of view that might warrant braking (for example, a dog running into the street), a collection of actions must be taken before the braking actually begins. First the driver must identify the event and decide if braking is necessary. Then the driver must lift his/her foot off the gas pedal and move it to the brake pedal. And finally, the driver must press the brake down its full distance in order to obtain maximum braking acceleration. The time to do all this is known as the reaction time. The distance traveled during this time is known as the reaction distance. Once the brakes are applied, the car begins to slow to a stop. The distance traveled by the car during this time is known as the braking distance. The braking distance is dependent upon the original speed of the car, the road conditions, and characteristics of the car such as its profile area, mass and tire conditions. Figure 1 shows the stopping distance for a Toyota Prius on dry pavement resulting from a 0.75-second reaction time. The reaction time of the driver is highly dependent upon the alertness of the driver. Small changes in reaction time can have a large effect upon the total stopping distance. Table 1 shows the reaction distance, braking distance, and total stopping distance for a Toyota Prius with an original speed of 50.0 mi/hr and varying reaction times.

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