
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.
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Chapter 2 Solutions
Physics For Scientists And Engineers: Foundations And Connections, Extended Version With Modern Physics
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