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Chapter 2: Q13CQ (page 79)

Is it possible for speed to be constant while acceleration is not zero? Give an example of such a situation.

Short Answer

Expert verified

Yes, it is possible in the case of uniform circular motion.

Step by step solution

01

Velocity and Acceleration

Keep in mind that speed and velocity are not interchangeable terms. Because velocity is a vector, it has a magnitude as well as a direction. The magnitude element of the velocity is called speed.

The change in velocity over time is referred to as acceleration.

There will be an acceleration if the magnitude (speed) or direction (direction) of the velocity changes.

02

Example where speed is constant, but acceleration is non-zero

An object traveling in a uniform circular motion would have a constant speed and centripetal acceleration (directed toward the center of the circle). Still, its velocity would not be constant since the object's motion direction is changing.

An item thrown straight up is another example. At the peak of its motion, it would have zero speed (the magnitude of the velocity is 0), but the change in velocity is not zero since the object's motion shifts from upward to downward.

Hence there are cases in which even speed is constant, but acceleration is possible only because of the direction component.

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Most popular questions from this chapter

a) A light-rail commuter train accelerates at a rate of\({\bf{1}}{\bf{.35}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\). How long does it take to reach its top speed of 80.0 km/h, starting from rest? (b) The same train ordinarily decelerates at a rate of\({\bf{1}}{\bf{.65}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\). How long does it take to come to a stop from its top speed? (c) In emergencies the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.30 s. What is its emergency deceleration in\({\bf{m/}}{{\bf{s}}^{\bf{2}}}\)?

If a subway train is moving to the left (has a negative velocity) and then comes to a stop, what is the direction of its acceleration? Is the acceleration positive or negative?

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\({\bf{0}}.{\bf{0500}}{\rm{ }}{\bf{m}}/{{\bf{s}}^{\bf{2}}}\)for\({\bf{8}}.{\bf{00}}{\rm{ }}{\bf{min}}\), starting with an initial velocity of\({\bf{4}}.{\bf{00}}{\rm{ }}{\bf{m}}/{\bf{s}}\)?

(b) If the train can slow down at a rate of\({\bf{0}}.{\bf{0500}}{\rm{ }}{\bf{m}}/{{\bf{s}}^{\bf{2}}}\), how long will it take to come to a stop from this velocity?

(c) How far will it travel in each case?

The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit\({\bf{1}}{\bf{.06 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\;{\bf{m}}\)in diameter. (a) If the average speed of the electron in this orbit is known to be\({\bf{2}}{\bf{.20 \times 1}}{{\bf{0}}^{\bf{6}}}{\bf{ m/s}}\), calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron鈥檚 average velocity?

On May 26, 1934, a streamlined, stainless steel diesel train called the Zephyr set the world鈥檚 nonstop long-distance speed record for trains. Its run from Denver to Chicago took 13hours,4minutes,58seconds , and was witnessed by more than a million people along the route. The total distance travelled was 1633.8km. What was its average speed in km/hand m/s?
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