Instant vs Time Interval

Lesson notes

A short written version of Lesson 3. The study sheet has more practice questions.

Short answer

"The 3rd second" is a time interval, not an instant. It is the stretch from t = 2 s to t = 3 s, so it lasts 1 s.

Key ideas

• In daily life, "time" means two things: a point in time or a stretch of time. Physics gives them two different names.
• An instant is a single point on the time axis. It marks when a motion starts or ends.
• A time interval is one segment of the time axis. It describes how long a motion lasts.
• There is no "0th second". The 1st second runs from 0 to 1. But time zero (t = 0) is an instant.
• The nth second runs from n−1 to n. If you get stuck, set n = 1 and check.
• "The first 3 s" is the stretch from 0 to 3. "The end of the 1st second" is the instant t = 1 s.

Step by step

1. An instant is one point on the time axis. A time interval is a segment of the axis.
2. Count seconds from 0. There is no 0th second, so 0 to 1 is the 1st second.
3. Then 1 to 2 is the 2nd second, and 2 to 3 is the 3rd second.
4. Check with the rule: the nth second runs from n−1 to n. With n = 3, it runs from 2 s to 3 s.
5. From 2 s to 3 s is a stretch that lasts 3 − 2 = 1 s. So the 3rd second is a time interval.

Common mistakes

• Calling the stretch 0 to 1 the "0th second". There is no 0th second. The stretch 0 to 1 is the 1st second.
• Thinking the nth second runs from n to n+1. Set n = 1: the 1st second is 0 to 1, so the nth second is n−1 to n.
• Mixing up "the first 2 s" and "the 2nd second". The first 2 s is 0 to 2. The 2nd second is only 1 to 2.
• Thinking a time given to the second, like 21:16:03, is an interval. It is still one point in time, so it is an instant.

Practice

Words in English and Chinese

instant

时刻

time interval

时间（间隔）

time axis

时间轴

time zero

0 时刻

the nth second

第 ns

the first 3 s

前 3s

the end of the 1st second

第 1s 末