Question

question 11 (5 points) a certain physical quantity has the units of miles/minute. what are the si units of the quantity? a) miles/hour b) meter/hour c) kilometer/second d) kilometer/hour e) meter/second

Explanation:

Step1: Recall SI units for length and time

SI unit for length is meter ($m$), SI unit for time is second ($s$). The given unit is miles/minute, which is a speed unit (length over time). We need to convert miles to meters and minutes to seconds, but first, let's analyze the options. Wait, actually, the question is about the SI units of the quantity (speed, since units are length/time). The SI unit for speed should be meter per second (m/s) or kilometer per hour? Wait no, SI base units: length is meter, time is second. So the SI unit for speed (length over time) is meter/second. Wait, but let's check the options. Wait, the options are: a) miles/hour, b) meter/hour, c) kilometer/second, d) kilometer/hour, e) meter/second.

Wait, the quantity has units miles/minute, which is a rate of length over time (speed). The SI units for length is meter, time is second. So we need to see which option is a length unit (in SI or derived) over a time unit (in SI or derived, but SI base time is second). Wait, SI unit for length: meter, time: second. So the SI unit for speed (length/time) is meter per second (m/s). Let's check the options:

a) miles/hour: miles is not SI, hour is not SI (SI time is second, minute, hour are not SI base, but hour is 3600 seconds).

b) meter/hour: hour is not SI time unit (SI time is second, so hour is 3600 s, but meter per hour is not SI unit for speed).

c) kilometer/second: kilometer is a derived SI unit (1 km = 1000 m), but meter is the base. However, kilometer per second is a valid unit but not the base SI unit for speed. Wait, no, the base SI unit for length is meter, time is second, so the SI unit for speed is meter per second (m/s), which is option e. Wait, but let's confirm: the SI unit for velocity (speed) is meter per second (m/s). So among the options, e) meter/second is the SI unit for speed (length/time) because meter is SI length, second is SI time.

Step2: Eliminate non-SI units or non-base combinations

• Option a: miles (non-SI length) and hour (non-SI time) → not SI.
• Option b: meter (SI length) but hour (non-SI time) → not SI unit for speed (SI time is second, minute, hour are not base, but second is base).
• Option c: kilometer (derived SI length) and second (SI time), but kilometer is 1000 meters, so kilometer/second is a valid unit but not the base SI unit (base is meter/second). Wait, no, the SI unit for speed is meter per second (m/s), which is option e.
• Option d: kilometer (derived SI length) and hour (non-SI time) → not SI.
• Option e: meter (SI length) and second (SI time) → this is the SI unit for speed (length over time), as meter is SI length, second is SI time.

Answer:

e) meter/second