Concept explainers
Two carts are set in motion at t = 0 on a frictionless track in a physics laboratory. The first cart is launched from an initial position of x = 18.0 cm with an initial velocity of 11.8î cm/s and a constant acceleration of –3.40î cm/s2. The second cart is launched from x = 20.0 cm with a constant velocity of 4.30î cm/s.
- a. N What are the times for which the two carts have equal speeds?
- b. N What are the speeds of the carts at that time?
- c. N What are the locations and times at which the carts pass each other?
- d. C What is the difference between what is asked in parts (a) and (c) of this problem with regard to the times you found?
(a)
Time at which two carts moves with same speed.
Answer to Problem 76PQ
Time at which two carts moves with same speed will be
Explanation of Solution
Write the Newton’s equation for velocity for the first cart.
Here,
Write the Newton’s equation for velocity for the second cart.
Here,
Equate the right hand sides’ of above equations.
Rewrite the above equation in terms of
Conclusion:
Substitute
Therefore, the time at which two carts moves with same speed will be
(b)
Speed of carts at that time.
Answer to Problem 76PQ
Both carts will be at the speed of
Explanation of Solution
It is given that the first cart is only accelerating. Second one is moving at fixed velocity,
Therefore, both carts will be at the speed of
(c)
The position and time when the carts pass each other.
Answer to Problem 76PQ
The time is
Explanation of Solution
Write the Newton’s equation for displacement of first cart.
Here,
Write the Newton’s equation for displacement of first cart.
Here,
Equate the right hand sides of above two equations.
Conclusion:
Substitute
Divide the above equation by
Rewrite the above equation in terms of
Substitute
Substitute
Therefore, the time is
(d)
The difference in meaning of question in part (a) and part (b).
Answer to Problem 76PQ
Part (a) asks to find the instant at which carts having same speed and part (b) asks to identify the time at carts will be at the same position.
Explanation of Solution
In part (a), it is asked to find the time at which both carts having the same speed and in part (b), it is asked to find the time at which both carts are at the same location.
From the starting point to a moment just before
Therefore, part (a) asks to find the instant at which carts having same speed and part (b) asks to identify the time at carts will be at the same position.
Want to see more full solutions like this?
Chapter 2 Solutions
Student Solutions Manual For Katz's Physics For Scientists And Engineers: Foundations And Connections, Volume 1
- A rock is thrown horizontally off a 56.0-m-high cliff overlooking the ocean, and the sound of the splash is heard 3.60 s later. If the speed of sound in air at this location is 343 m/s, what was the initial velocity of the rock?arrow_forwardA driver uniformly accelerates his car such that a=6.851im/s2. a. Assuming he starts from rest, find the velocity of the car after it has accelerated for 4.55 s. b. If immediately after that 4.55 s the driver lays off the accelerator, slams on the brakes, and comes to a stop in the subsequent 5.62 s, what is the acceleration he experiences during that time, assuming the acceleration is constant?arrow_forwardTadeh launches a model rocket straight up from his backyard that takes 4.50 s to reach its maximum altitude. (After launch, the rockets motion is only influenced by gravity.) a. What is the rockets initial velocity? b. What is the maximum altitude reached by the rocket?arrow_forward
- In a cartoon program, Peter tosses his baby, Stewie, up into the air to keep the child entertained. Stewie reaches a maximum height of 0.873 m above the release point. Suppose the positive y axis points upward, a. With what initial velocity was Stewie thrown? b. How much time did it take Stewie to reach the peak height?arrow_forwardAn unwary football player collides with a padded goalpost while running at a velocity of 7.50 m/s and comes to a full stop after compressing the padding and his body 0.350 m. (a) What is his acceleration? (b) How long does the collision last?arrow_forwardCars A and B each move to the right with constant acceleration along a straight road. The velocity vectors of each car are shown in Figure P2.78 for several times separated by equal time intervals. For the entire interval from time t1 to time t4, car B is ahead of car A (that is, car B is to the right of car A), a. Is the acceleration of car B to the left, to the right, or zero? Explain. b. Is the magnitude of the acceleration of car A greater than, less than, or equal to the magnitude of the acceleration of car B? Explain your reasoning, c. Is the distance between car A and car B at time t3 greater than, less than, or equal to the distance between car A and car B at time t2? Explain.arrow_forward
- During a relay race, you run the first leg of the race, a distance of 2.0 102 m to the north, in 22.23 s. You then run the same distance back to the south in 24.15 s in the second leg of the race. Suppose the positive y axis points to the north. What is your average velocity a. for the first leg of the relay race and b. for the entire race?arrow_forwardIn the movie Star Wars: The Empire Strikes Back, after being told that Darth Vader is his father, Luke Skywalker falls from a ledge in Cloud City (not on the Earth, so the magnitude of the free-fall acceleration is not necessarily 9.81 m/s2). Suppose he falls a distance of 28.5 m in 2.5 s. Assuming he starts from rest, answer the following questions. a. What is Lukes velocity 2.5 s after he starts to fall? b. What is the constant acceleration due to gravity, experienced by Luke, on Cloud City? Use an upward-pointing y axis.arrow_forwardA cyclist travels from point A to point B in 10 mm. During the first 2.0 mm of her trip, she maintains a uniform acceleration of 0.090m/s2 . She then travels at constant velocity for the next 5.0 nun. Next, she decelerates at a constant rate so that she cons to a rest at point B 3.0 mm later. (a) Sketch the velocity-versus-tine graph for the trip. (b) What is the acceleration during the last 3 mm? (c) How far does the cyclist travel?arrow_forward
- Freight trains can produce only relatively small accelerations and decelerations. (a) What is the final velocity of a freight train that accelerates at a rate of 0.0500 m/s2 for 8.00 min, starting with an initial velocity of 4.00 m/s? (b) If the train can slow down at a rate of 0.550 m/s, how long will it take to come to a stop from this velocity? (c) How far will it travel in each case?arrow_forwardPete and Sue, two reckless teenage drivers, are racing eastward along a straight stretch of highway. Pete is traveling at 98.0 km/h, and Sue is chasing him at 125 km/h. a. What is Petes velocity with respect to Sue? b. What is Sues velocity with respect to Pete? c. If Sue is initially 325 m behind Pete, how long will it take her to catch up to him?arrow_forwardA trooper is moving due south along the freeway at a speed of 21 m/s. At time t = 0, a red car passes the trooper. The red car moves with constant velocity of 28 m/s southward. At the instant the troopers car is passed, the trooper begins to speed up at a constant rate of 2.0 m/s2. What is the maximum distance ahead of the trooper that is reached by the red car?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax CollegeUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning