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). a) At some moment the truck's momentum is 48300 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) ______________. b) This means that as the truck travels, the truck's momentum (in kg · m/s) is always ______________ times as large as the truck's speed (in m/s). c) If the truck is traveling at 17 m/s, what is the momentum (in kg m/s) ______________.

Answer 1

The momentum of a truck is proportional to its speed. At a certain moment, the truck's momentum is 48300 kg · m/s and its speed is 23 m/s, making the momentum 2100 times larger than the speed. This relationship remains constant as the truck travels. If the truck is traveling at 17 m/s, its momentum would be 35700 kg · m/s.

Step-by-step explanation:

In this case, the momentum of the truck is proportional to its speed. We can use the formula for momentum, which is given by:

momentum = mass x velocity

Let's use the given information to solve each part of the question:

a) At the given moment, the truck's momentum is 48300 kg · m/s and its speed is 23 m/s. To find how many times larger the momentum is compared to the speed, we divide the momentum by the speed: 48300 kg · m/s / 23 m/s = 2100 times larger.

b) Since momentum is proportional to speed, the truck's momentum will always be the same number of times larger than its speed. This means that as the truck travels, the truck's momentum is always 2100 times as large as its speed.

c) If the truck is traveling at 17 m/s, we can use the proportionality to find its momentum. Using the previous result, we know that the momentum is 2100 times larger than the speed, so the momentum would be: 17 m/s x 2100 = 35700 kg · m/s.

Answer 2

a) 2100, b) 2100, c)
`p = 35700\,(kg\cdot m)/(s)`

Step-by-step explanation:

a) At some moment the truck's momentum is 48300 kg · m/s and the truck's speed is 23 m/s. At this moment, truck's momentum (in kg · m/s) is how many times as large as the truck's speed (in m/s):

`i = (48300\,(kg\cdot m)/(s) )/(23\,(m)/(s) )`

`i = 2100`

b) This means that as the truck travels, the truck's momentum (in kg · m/s) is always 2100 times as large as the truck's speed (in m/s).

c) If the truck is traveling at 17 m/s, what is the momentum (in kg m/s):

`p = (17\,(m)/(s) )/(23\,(m)/(s) ) \cdot \left(48300\,(kg\cdot m)/(s) \right)`

`p = 35700\,(kg\cdot m)/(s)`