Concept explainers
(a)
The time interval during which the bicycle is ahead of the car.
(a)
Answer to Problem 38P
The time interval during which the bicycle is ahead of the car is
Explanation of Solution
Write the
Here,
Rewrite the above equation for
Use the above equation to write the expression for the time taken by the bicycle to reach its maximum speed.
Here,
It is given that the acceleration of the car is less than the acceleration of the bicycle. This implies the car cannot catch the bicycle until the time bicycle is at its maximum speed and coasting and it will be greater than the time taken by the bicycle to reach its maximum speed.
Write the equation for the total displacement of the bicycle.
Here,
It is given that the car starts from rest so that its initial velocity will be zero.
Write the equation for the displacement of the car during the time taken by the bicycle to reach the car.
Here,
When the car catches the bicycle, the two displacements will be equal.
Write the condition when the car to catches the bicycle.
Conclusion:
Substitute
Substitute
Substitute
Put equations (V) and (VI) in equation (IV).
Write the quadratic formula to solve the equation
Equation (VII) is a quadratic equation in
Since
Therefore, the time interval during which the bicycle is ahead of the car is
(b)
The maximum distance by which the bicycle leads the car.
(b)
Answer to Problem 38P
The maximum distance by which the bicycle leads the car is
Explanation of Solution
The distance by which bicycle will lead the car will increase as long as the bicycle moves faster than the car or when the speed of the car becomes equal to the maximum speed of the bicycle.
Write the equation for the elapsed time when the bicycle’s lead ceases to increase.
Here,
Write the equation for the lead of the bicycle.
Here, the subscript
Put equations (V) and (VI) in the above equation.
Conclusion:
Substitute
Substitute
Therefore, the maximum distance by which the bicycle leads the car is
Want to see more full solutions like this?
Chapter 2 Solutions
Principles of Physics: A Calculus-Based Text
- A person is driving along a straight highway at a speed of 22.0 m/s when the traffic light which is 40.0 m ahead turns yellow. Because of his "reaction time", there is a delay of 0.13 seconds before the man steps on the brake. The car then slows with a deceleration of 4.30 m/s. By how much distance does the driver miss the traffic light line?arrow_forwardYou drive a beat-up pickup truck along a straight road for 8.4 km at 70 km/h, at which point the truck runs out of gasoline and stops. Over the next 30 min, you walk another 2.0 km farther along the road to a gasoline station. (a) What is your overall displacement from the beginning of your drive to your arrival at the station?arrow_forwardTwo cars both cover a straight distance, d = 223 m, in time t = 19.5 s. Car A moves at a constant velocity (vA). Car B moves at a constant acceleration (aB), starting from an initial velocity of vOB = 7.6 m/s. Assume both cars are moving in the positive x-direction. Part (a) What is the velocity of Car A? Part (b) What is the final velocity of Car B? What is the acceleration of Car B?arrow_forward
- A blue car travels down a straight road at a constant speed of 18.8 m/s. As they pass a red car, initially stopped on the side of the road, the red car speeds up at a rate of 1.77 m/s2. How much distance (in m) does the red car travel before it overtakes the blue car?arrow_forwardStarting from rest at home plate, a baseball player runs to first base (90 ft away). He uniformly accelerates over the first 10.7 ft to his maximum speed, which is then maintained until he crosses first base. If the overall run is completed in 3.4 seconds, determine his maximum speed, the acceleration over the first 10.7 feet, and the time duration of the acceleration. t = 0 Answers: Vmax a = 10.7 t= i i i 79.3' t = 3.4 sec ft/sec ft/sec² secarrow_forwardA football player, starting from rest at the line of scrimmage, accelerates along a straight line for a time of 4.60 s. Then, during a negligible amount of time, he changes the magnitude of his acceleration to a value of 1.04 m/s². With this acceleration, he continues in the same direction for another 2.29 s, until he reaches a speed of 6.66 m/s. What is the value of his acceleration (assumed to be constant) during the initial 4.60 -s period? Number Unitsarrow_forward
- A sprinter accelerates from rest to a top speed with an acceleration whose magnitude is 3.70 m/s2. After achieving top speed, he runs the remainder of the race without speeding up or slowing down. The total race is fifty meters long. If the total race is run in 7.00 s, how far does he run during the acceleration phase?arrow_forwardA police car is traveling at a velocity of 16.0 m/s due north, when a car zooms by at a constant speed of 50 m/s due north. After a reaction time of 0.700 s the policeman begins to pursue the speeder with an acceleration of 5.00 m/s2. Including the reaction time, how long does it take for the police car to catch up with the speeder?arrow_forwardA blue car travels down a straight road at a constant speed of 18.9 m/s. As they pass a red car, initially stopped on the side of the road, the red car speeds up at a rate of 2.01 m/s2. How much distance (in m) does the blue car travel before the red car overtakes the blue car?arrow_forward
- A car is moving with a speed of 32.0 m/s. The driver sees an accident ahead and slams on the brakes, causing the car to slow down with a uniform acceleration of magnitude 3.50 m/s2. How far does the car travel after the driver put on the brakes until it comes to a stop?arrow_forwardI am having trouble finding the average velocity of a truck in a problem. The problem states, "A truck on a straight road starts from rest, accelerating at 2.00 m/s2 until it reaches a speed of 20.0 m/s. Then the truck travels for 60.0 s at constant speed until the brakes are applied, stopping the truck in a uniform manner in an additional 5.00 s." I know that the truck is in motion for 75 seconds and I know that average velocity is displacement/time but I havent been able to get the right number.arrow_forwardA driver traveling at night on a country road suddenly sees another car pull out into the roadway in front of him.He slams on his brakes and skids for a distance of 72.9 m until he hits the other car. If the driver slowed with constant acceleration of 4.8m/s² for 4.5 s,with what speed would he hit the other car?arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON