Physics 198 Homework 2

Physics 198 Homework 2

1. What is the difference between a longitudinal and a transverse wave? Give an example of each.

Solution:

The difference is that in longitudinal waves the motion of the medium is parallel to the direction of wave travel, while in transverse waves the motion of the medium is perpendicular to the direction of wave travel. A sound wave in air is longitudinal wave. A wave on a rope shaken up and down at one end is transverse wave.

1. A slope of a graph of distance versus time is equal to what quantity?

Solution:

The slope of a graph of position versus time is equal to the speed.

1. Can an object have zero velocity and nonzero acceleration at the same time? Give examples.

Solution:

If an object is at the instant of reversing direction (like an object thrown upward, at the top of its path), it instantaneously has a zero velocity and a non-zero acceleration at the same time. A person at the exact bottom of a “bungee” cord plunge also has an instantaneous velocity of zero but a non-zero (upward) acceleration at the same time.

1. Which one of these motions is not at constant acceleration: a rock falling from a cliff, an elevator moving from the second floor to the fifth floor making stops along the way, a dish resting on a table?

Solution:

The elevator moving from the second floor to the fifth floor is NOT an example of constant acceleration. The elevator accelerates upward each time it starts to move, and it accelerates downward each time it stops.

Ignoring air resistance, a rock falling from a cliff would have a constant acceleration. (If air resistance is included, then the acceleration will be decreasing as the rock falls.) A dish resting on a table has an acceleration of 0, so the acceleration is constant.

5.A sprinter accelerates from rest to in 1.35 s. What is his acceleration

(a) in and (b) in (c) Compare this to the acceleration of on object in free fall.

Solution:

The average acceleration of the sprinter is

(a).

(b)

(c)The acceleration of an object in free fall is:

So,

1. A rolling ball moves from to during the time from to What is its average velocity?
   

Solution:

The average velocity is given by.

1. A sports car moving at constant speed travels 110 m in 5.0 s. If it then brakes and comes to a stop in 4.0 s, what is its acceleration in Express the answer in terms of “g’s,” where

Solution

The initial speed of the car before it accelerates is:

The final speed is, and the time to stop is 4.0 s. The acceleration is:

1. Figure below shows the velocity of a train as a function of time. (a) At what time was its velocity greatest? (b) During what periods, if any, was the velocity constant? (c) During what periods, if any, was the acceleration constant? (d) When was the magnitude of the acceleration greatest?

Solution:

Slightly different answers may be obtained since the data comes from reading the graph.

(a) The greatest velocity is found at the highest point on the graph, which is at .

(b) The indication of a constant velocity on a velocity-time graph is a slope of 0, which occurs from .

(c) The indication of a constant acceleration on a velocity-time graph is a constant slope, which occurs from , again from , and again from .

(d) The magnitude of the acceleration is greatest when the magnitude of the slope is greatest, which occurs from .

1. If and , determine the magnitude and direction of .

Solution:

The magnitude is

.

If is the angle between and x-direction then

.

From this follows: .

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