Question

which of the following best represents the speed of a sloth?
a. $4 \times 10^5$ kilometers per second
b. $4 \times 10^{-5}$ meters per second
c. $4 \times 10^{-5}$ kilometers per second

Explanation:

Step1: Analyze Option A

$4\times10^{5}$ kilometers per second is an extremely high speed, comparable to the speed of light (about $3\times10^{5}$ km/s), which is impossible for a sloth.

Step2: Analyze Option B

First, convert $4\times10^{-5}$ meters per second to a more intuitive unit. We know that 1 meter per second = 3.6 kilometers per hour. So $4\times10^{-5}$ m/s = $4\times10^{-5}\times3.6$ km/h = $1.44\times10^{-4}$ km/h, which is a very slow speed, consistent with a sloth's speed.

Step3: Analyze Option C

$4\times10^{-5}$ kilometers per second = $4\times10^{-5}\times1000$ meters per second = 0.04 meters per second, and converting to km/h: 0.04×3.6 = 0.144 km/h. Wait, no, wait, $4\times10^{-5}$ km/s is 0.04 m/s, but let's check the magnitude. A sloth's speed is very slow, but let's re - check the units. Option B is in m/s, $4\times10^{-5}$ m/s is 0.00004 m/s, and Option C is $4\times10^{-5}$ km/s = 0.04 m/s. Wait, maybe I made a mistake earlier. Let's recall the actual speed of a sloth: a sloth moves at a speed of about 0.15 meters per minute, which is 0.15/60≈0.0025 m/s. Wait, maybe my initial conversion was wrong. Let's start over.

1. Option A: $4\times10^{5}$ km/s is way too fast (speed of light is ~$3\times10^{5}$ km/s), so A is out.
2. Option B: $4\times10^{-5}$ m/s. Let's convert to meters per minute: $4\times10^{-5}\times60 = 2.4\times10^{-3}$ m/min, which is very slow, but maybe too slow? Wait, no, maybe I messed up the actual sloth speed. Wait, a sloth's speed is about 0.2 - 0.3 meters per minute, which is about 0.003 - 0.005 m/s. Wait, $4\times10^{-5}$ m/s is 0.00004 m/s, which is too slow. Wait, maybe the options have a typo? Wait, no, let's check the units again. Option C: $4\times10^{-5}$ km/s. 1 km = 1000 m, so $4\times10^{-5}$ km = 0.04 m, so $4\times10^{-5}$ km/s = 0.04 m/s. Option B: $4\times10^{-5}$ m/s = 0.00004 m/s. Wait, maybe the correct option is B? Wait, no, maybe I confused the exponents. Wait, let's check the order of magnitude. A sloth's speed is very slow. Let's consider the scientific notation. Option B is $4\times10^{-5}$ m/s, which is 0.00004 m/s, and Option C is $4\times10^{-5}$ km/s = 0.04 m/s. The actual speed of a sloth is around 0.003 m/s (about 0.18 meters per minute). So $4\times10^{-5}$ m/s is 0.00004 m/s, which is slower than the actual, but Option C is 0.04 m/s, which is faster. Wait, maybe the question has a mistake, but among the options, Option B is the slowest reasonable speed (since A is too fast, C is faster than B, but B is in m/s and has a smaller magnitude). So the correct option is B.

Answer:

B. $4\times10^{-5}$ meters per second