Instant vs Time Interval

Is there a "0th second"? (preview)

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Note: there is no "0th second," as the time axis starts at 0. So the very first stretch, from 0 to 1, is the 1st second. There is no 0th second. Now instants. Instants do have zero. That point is zero: time zero. Hi, everyone! In this video, we continue our full course.

In this lesson: why time intervals and instants matter

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Today: time interval and instant. We began with many concepts, such as the particle in Lesson 1, the reference frame in Lesson 2, and today's topic. They all prepare us to study kinematics. What is kinematics? Simply put, how an object moves. To study how an object moves, you first need to know what is moving. That's the particle model. Real objects come in all shapes, which is a hassle. To simplify, we use particles, treating objects as moving points. A moving point is easy to calculate. That's why we use the particle model. To tell if an object is moving, which we covered in Lesson 2, isn't easy. Why? Motion is absolute; rest is relative. Everything is moving. What matters isn't whether it truly moves, but whether it moves in our problem. How to decide? We need a reference frame. We pick an object and call it at rest, then look at our object: does it move relative to your frame?

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That's what a reference frame does: it tells us if an object is moving. Once we know whether it moves, we want to know when it starts, when it stops, and for how long. To study these questions, we need time intervals and instants.

The three goals of this lesson

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So you won't end up confused, just in one ear and out the other, not sure what you learned, here are today's three goals. Goal 1: know the difference between a time interval and an instant. Goal 2: know the common ways of saying time intervals and instants. A key Grade 10 exam topic. Goal 3: given a time axis, mark a time interval or instant on it. Or, given a marked time axis, say which interval or instant it shows. Those are today's three goals. Let's start with the definitions of interval and instant. Time is closely tied to daily life. We say "time, time, time" every day. No time to study, want to play, no time to sleep, short sleep: all "time." To sort out time interval and instant, let's first read a primary

A kid's diary: what does "time" mean?

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school "outstanding diary." A pupil wrote it, apparently true. "Dad, I Have Something to Tell You" When you read this, it's already 5:00. I honestly can't stand you. For the last two days, 7 a.m. to midnight, over ten hours straight, you kept shouting "ball, ball, ball." Sometimes you yell at night. At 3 a.m. I woke up scared, and needed 30 min to fall asleep. I'm done with you. I even slept 40 minutes in math class! Warning: if you watch the World Cup again, I'm truly done, I'll call neighbor Uncle Wang "Dad"! End. Never mind the story between the kid, his dad, and Uncle Wang. Not what physics is about. Ethics or sociology might study that. Now look closely at the words I marked in red and blue. Which are red? 5 a.m. and 3 a.m. Look: do both record a point in time? Dad read the letter at 5 a.m., the kid woke up at 3 a.m.

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Similarly, say you and your girlfriend agreed to see a movie tomorrow at 2:30 p.m. Even one second late counts as late, and the consequences could be serious. So is 2:30 a point in time? The one you agreed on. Now the blue parts: last two days, 7 a.m. to midnight, Over ten hours: all stretches of time? In daily speech, all are called "time." In daily life, "time" has two meanings. Sometimes a point in time, sometimes a time interval. We're used to it, so there's no ambiguity. Say "see you at 2:30 tomorrow": 2:30 is clearly a point. No need to stress it's a point, not a stretch. Everyone knows. But physics is a rigorous subject, so point and stretch each get their own name.

Definitions: instant vs. time interval

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They are instant and time interval. An instant is a point in time. On the time axis, it is one point. It records when a motion starts or ends. Take a photo, for example: it records what happened at that instant. What we usually call "time" is really a time interval. "Time" and "time interval" mean the same. It's a stretch on the time axis, like from 3 to 4. Physically, it's how long a motion lasts. One second, an hour, a day, three days and nights: all time intervals. So we must tell them apart. An instant is a point; a time interval is a stretch. Try a problem.

Example 1: which one is a time interval?

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These often appear in school exams. It asks which involve a time interval and which involve an instant. This one asks which is a time interval. Remember: a time interval is a stretch, not a point. One by one. A: CCTV news broadcast lasts 30 minutes. Is that a time interval? Yes, from 7:00 to 7:30 p.m. It's a time interval. A is correct. B: At 0:00 on July 1, 1997, the Hong Kong handover took effect. That should be an instant. After 0:00 on July 1, the handover took effect. An instant, not an interval. So B is wrong. C: The Olympics opened at 8 p.m. on Aug. 8, 2008. Also an instant. Right after 8 p.m., the Games began. So it's an instant. D: a time given to the second, for the launch of Tiangong-1. Also an instant: it launched at that time. Many students get stuck: C has no seconds, but D does. Both are just instants.

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Read C as 8:00:00 p.m. Writing the zero seconds looks silly, so we omit them. Anyone who has learned to read can read it. B, C, D are all instants. Only A: a time interval. Get fluent: given a description, tell if it is a time interval or instant. That's our first goal.

Common phrases for intervals and instants

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Now that we can tell them apart, let's look at the common phrases for each, and how to mark them on the time axis. Both are so common in daily life that we have many ways to say them. For time intervals: the 1st second, the 3rd, first 3 s, nth second. These are all time intervals. Note: there is no "0th second," as the time axis starts at 0. So the very first stretch, from 0 to 1, is the 1st second. There is no 0th second. Now instants. Instants do have zero. That point is zero: time zero. Also the start and end of the 1st second, and of the nth second. The 1st second's start is its first point, so it's an instant. The end is its last point: an instant too. Those are the common phrases for both. Now let's mark them on the time axis.

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Time intervals first. The 1st second is from 0 to 1. The 3rd second: this is the 1st, this is the 2nd, so this is the 3rd. So the 3rd second is this stretch. Next, the first 3 s: three seconds counted from the very start. That should be this whole stretch. This is the first 3 seconds.

The nth second and the n = 1 trick

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Then the nth second trips many people up. Is it from n to n+1, or from n-1 to n? Memorize it? No need. Here is a trick. Can't work out the nth second? Look at the 1st second. is it from 0 to 1, or 1 to 2? We said earlier it's from 0 to 1. So here, n = 1. Then this point is n, and this is n-1. So the nth second is from n-1 to n. That's the nth second. Stuck on "the nth…" or "the first n…"? Just set n = 1, that's it. You'll instantly see whether it's n-1 to n or n to n+1. That's the time intervals done.

Marking instants on the time axis

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Now the instants. Time zero is this point. The 1st second's start is this point too, so it's identical to time zero. And the end of the 1st second? The end of the 0-to-1 stretch, this point, is the end of the 1st second. The start of the nth second? First, mark the nth second. We said it runs from n-1 to n. So its start is the point n-1. That's the start of the nth second. End of the nth second? It's this point. That's the end of the nth second. Intervals and instants are all marked. Two things to note. First, Seconds are counted from the 1st, not the 0th. The earliest is the 1st second: 0 to 1. Second, the tricky part: the nth second and its start or end. Remember: it's n-1 to n.

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Forget? Set n = 1 and work it out. Easy. Now, a few more problems.

Example 2: statements on a time axis

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Which statement on this time axis is true? A says t2, this point, is an instant. That's fine. It's the end of second 2, or start of second 3. Also called "within 2 seconds," note that last part. "Within 2 seconds" means an interval. So it's wrong. A point is an instant, so it can't be a time interval. They conflict, so A is wrong. B: 2 to 3 is this stretch. It's a time interval: it's a stretch. Called "the 3rd second." Can't see it? Count from zero: 1st second, 2nd, 3rd. It's the 3rd second. B is correct. C: from 0 to t2 is a time interval, "the first 2 seconds" or "the 2nd second." Let's draw 0 to t2. It's this stretch. It's a time interval, no doubt, and "the first 2 seconds" is fine, but it isn't "the 2nd second." The 2nd second is just 1 to 2, this stretch. So C is wrong.

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D: t(n-1) to tn is a time interval, called "the (n-1)th second." Another n! Whenever a t has an n in it, set n = 1 and plug it in. When n = 1, n-1 is 0, so t(n-1) is t0. tn is t1, and the (n-1)th becomes the 0th. In other words, option D reads: t0 to t1, a time interval, the 0th second. That can't be. There's no 0th second. As I said, seconds start from the 1st, so the smallest is the 1st second. Change n-1 to n here and it's right. Change n-1 to n and plug in 1: t0 to t1 is a time interval, called the 1st second. Fine. Questions with an n? Plug in n = 1 and check. The answer is B. Did you master the opening three goals?

Summary

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Goal 1: the difference is simple: an instant is a point, a time interval is a stretch. Goal 2: Master the common phrases. 1st second, 3rd second, first 3 seconds, nth second, during the nth second, the first few seconds, all time intervals. Time zero, start of the 1st second, the end of the 1st second: all instants. Know them: tell interval from instant. Goal 3: given a time axis, mark intervals and instants. I did this several times in the examples. Not fluent yet? Just listen again.