Question

A truck is speeding up as it travels on an interstate. The truck's momentum (in kg · m/s) is proportional to the truck's speed (in m/s).At some moment the truck's momentum is 50600 kg · m/s and the truck's speed is 23 m/s. At this moment, the truck's momentum (in kg · m/s) is how many times as large as the truck's speed (in m/s)?IncorrectThis means that as the truck travels, the truck's momentum (in kg · m/s) is always Incorrect times as large as the truck's speed (in m/s).If the truck is traveling at 16 m/s, what is the truck's momentum?

Answer 1

Answer:

At the moment, the truck's momentum (in kg · m/s)  is 2200 times as large as the truck's speed (in m/s).

This means that as the truck travels, the truck's momentum (in kg · m/s) is always 2200 times as large as the truck's speed (in m/s).

If the truck is travelling at 16 m/s, the truck's momentum is 35200 kg · m/s.

Explanation:

From the question,

The truck's momentum (in kg · m/s) is proportional to the truck's speed (in m/s).

Let the truck's momentum be P and the truck's speed be v,

Then  we can write that

P∝v

Then,

P = kv

Where k is the proportionality constant

From the question,

At some moment the truck's momentum is 50600 kg · m/s and the truck's speed is 23 m/s,

To determine how many times the truck's speed is as large as the truck's momentum at this moment, we will divide the truck's momentum by the speed, that is

50600 ÷ 23 = 2200

Hence, at the moment, the truck's momentum (in kg · m/s)  is 2200 times as large as the truck's speed (in m/s).

Since, dividing the truck's momentum by the truck's speed gives the proportionality constant k (that is, P/v = k), then

This means that as the truck travels, the truck's momentum (in kg · m/s) is always 2200 times as large as the truck's speed (in m/s).

From

P = kv

Then, k = P/v

At a moment, P = 50600 kg · m/s and v = 23 m/s

∴ k = 50600 kg · m/s ÷ 23 m/s = 2200 kg

k = 2200 kg

To determine the truck's momentum if the truck is traveling at 16 m/s

From

P = kv

k = 2200 kg

v = 16 m/s

∴ P = 2200 kg × 16 m/s

P = 35200 kg · m/s

Hence, if the truck is travelling at 16 m/s, the truck's momentum is 35200 kg · m/s.