A car is at rest on the middle of an eastbound single-lane road while the driver...
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A car is at rest on the middle of an eastbound single-lane road while the driver (Bill) of the car is lost and studying a map. A large hungry dinosaur (T-Rex) is running with constant speed (Va) eastbound along the same road toward the car. Bill sees the dinosaur running toward his car and so he quickly puts his foot on the throttle of the car, which causes the car to speed up in the eastbound direction with constant acceleration (A) in an attempt to outrun the dinosaur and avoid being eaten. At the moment the throttle is activated, there is a distance (D) between the car and the dinosaur. Luckily, Bill narrowly escapes being captured. a) Draw a qualitative graph of position vs. time for both the car and the dinosaur and a qualitative graph of velocity vs. time for both the car and the dinosaur. Assume eastbound is the positive direction and label each part of the graph. b) Determine an expression for the time interval (T) starting from moment the car begins speeding up to the moment the dinosaur nearly catches the car (in terms of only V and A). c) Determine an expression for D in terms of only V and A. d) In a 1st scenario, A = 5.0 m/s and V = 7.0 m/s. What are the values of T and D? e) In a 2nd scenario, Va = 14 m/s and D is unchanged from that of the 1st scenario. What is the value of A in the 2nd scenario? A car is at rest on the middle of an eastbound single-lane road while the driver (Bill) of the car is lost and studying a map. A large hungry dinosaur (T-Rex) is running with constant speed (Va) eastbound along the same road toward the car. Bill sees the dinosaur running toward his car and so he quickly puts his foot on the throttle of the car, which causes the car to speed up in the eastbound direction with constant acceleration (A) in an attempt to outrun the dinosaur and avoid being eaten. At the moment the throttle is activated, there is a distance (D) between the car and the dinosaur. Luckily, Bill narrowly escapes being captured. a) Draw a qualitative graph of position vs. time for both the car and the dinosaur and a qualitative graph of velocity vs. time for both the car and the dinosaur. Assume eastbound is the positive direction and label each part of the graph. b) Determine an expression for the time interval (T) starting from moment the car begins speeding up to the moment the dinosaur nearly catches the car (in terms of only V and A). c) Determine an expression for D in terms of only V and A. d) In a 1st scenario, A = 5.0 m/s and V = 7.0 m/s. What are the values of T and D? e) In a 2nd scenario, Va = 14 m/s and D is unchanged from that of the 1st scenario. What is the value of A in the 2nd scenario?
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