Explain or Exemplify

[Note:You Must Be Interested In Physics.]

If you agree with a statement, given an example. If you disagree, give an explanation.

[Try To Be As Elementary As Possible.]

Can a body have zero velocity and still be accelerating?
Can a body have a constant speed and still have varying velocity?
Can a body have a constant velocity and still have varying speed?
Can an object have eastward velocity while experiencing a westward acceleration?
Can the direction of the velocity of a body change when its acceleration is constant?

#Physics

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

This is basically Newton's Laws in action. Just think of a heavy crate sliding on a floor. We know from the second law that $a=\frac{F_{net}}{m}$ . And acceleration is defined as the rate of change of velocity (yes, that includes direction). So, a crate can be sliding or not sliding, and at all times you can be pushing it, giving it an acceleration. You may not change how fast its moving, but you may change its direction of motion.

3 eh is sort of complicated;

For the most part, the answer is NO. This is because velocity is (simply) defined as speed with direction; so, if speed varies, so does velocity.

If we analyze the two parameters in terms of their definitions and take a further look by looking at their integrals, then incorporating some knowledge of quantum mechanics we can have a theoretical "yes" to that:

While in the purely mathematical world the answer is still no, in the real world, with weird relativity laws and quantum mechanics plethora we could squeeze something out. For example, a virtual particle under an infinite timewarp, say near a black hole, when observed from the same frame of reference, may skip between 5D branes in under the planck time, but in the 4D reference only travel 1 $c$ s, but, as far as the total distance traveled goes, its speed is greater while its velocity, or net speed with direction may remain the same.

Dunno. Honestly I thought about this for like an hour and couldn't come up with anything better ;P

Let's just say NO and end the day there :)

John M. - 6 years, 7 months ago

Ok. & Wow!

I don't know anything about quantum mechanics.You could probably post some articles explaining quantum to those who have null knowledge in that field [like the article at JohnExplainsTheUniverse]

I didn't notice that Arusimha had changed his comment and included reasons as well as example [cuz at 1st he didin't]

in 4 we can also have spring motion,can't we??? and oscillatory also.

Soumo Mukherjee - 6 years, 7 months ago

eh we can have anything. if we have a crate sliding left on a floor that has friction, it is already decelerating - or, accelerating towards right - or, losings its leftward velocity and gaining rightward. Now if instead of friction we had something else pushing it at all times, then after the crate stopped it would continue accelerating towards right and gain a positive velocity towards right.

-oh, and the quickest way to become a quantum mechanics Big G is to watch THIS playlist - in order.

You can take it easy one a day - or one a week.

Enjoy :)

John M. - 6 years, 7 months ago

@John M. – The friction example is an ingenious and original one. That example is very rare and hard to spot.

Ok i will watch them.

Thanx @John Muradeli .

Soumo Mukherjee - 6 years, 7 months ago

@John M. – didn't get it

Nafij Shaikh - 6 years, 7 months ago

Yes. A body thrown upwards at its max height has zero velocity and also has acceleration due to gravity.
Yes. A body moving in with uniform circular motion has constant speed but change in direction. So it moves with varying velocity
No. A body moving with constant velocity has no change in direction or speed.
Yes. East and west are opposite directions. So when a body is thrown upwards, its velocity is up while acceleration is downwards.

Arunsimha Reddy - 6 years, 7 months ago

If you are answering 'No', please explain 'why No?'

If you are answering 'Yes', then please 'Give An Example.'

Soumo Mukherjee - 6 years, 7 months ago

Yes - Projectile thrown vertically at maximum height.
Yes - Uniform circular motion.
No - If velocity is constant, its magnitude (that is speed) and direction both are constant.
Yes - Projectile is projected eastwards, wind gives it westward acceleration.
Yes - Projectile's velocity changes around the maximum height even though acceleration is constant.

Abhishek Sharma - 6 years, 7 months ago

5th one was good

Ujjwal Mani Tripathi - 4 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$