Motion at changing speeds Constant acceleration In this task you will examine the motion of a vehicle accelerating at a constant rate, which means that its time-velocity graph is a linear function. The objective of the task is to describe the function representing the dependence of vehicle position on time. In the dynamic figure below, the Constant acceleration tool was used to create a simulation of a red car that accelerates for a duration of 10 seconds from a stationary position to a speed of 30 meters per second (108 kilometers per hour). The "average motion" Use the Constant acceleration tool to create a simulation of the red car and of another car moving at a constant velocity, with a motion similar to that of the red car in the following ways: - It starts to move at the same time and position as the red car. - After 10 seconds the two cars reach the same position. Compare the velocities of the two cars: which of them travels faster and when? Create a simulation of another car, also traveling at a constant speed and starting at the same time and position as the red car, but with both cars reaching the same position after 6 seconds. What is the speed of the new car? Without creating a simulation, try to conjecture about the speed of a car traveling at constant velocity and starting at the same time and position as the red car, so that the two cars reach the same position after 8 seconds. Assuming your conjecture is right, calculate the position at which the two cars will meet. Check your conjectures with a simulation. Describe a method for computing the position of the red car after any number of seconds. Describe the time-velocity graph of the red car using a correspondence rule. Describe the time-position graph of the red car using a correspondence rule. time-velocity graph time-position graph initial position initial velocity acceleration grid 1 2 3 graph width duration of motion (seconds): clock (seconds) step: trace

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