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Cars A and B are racing each other along the same straight road in the following manner: Car A has a head start and is a distanc

4vir4ik [10]

The question is incomplete. Here is the complete question.

Cars A nad B are racing each other along the same straight road in the following manner: Car A has a head start and is a distance $D_{A}$ beyond the starting line at t = 0. The starting line is at x = 0. Car A travels at a constant speed $v_{A}$ . Car B starts at the starting line but has a better engine than Car A and thus Car B travels at a constant speed $v_{B}$ , which is greater than $v_{A}$ .

Part A: How long after Car B started the race will Car B catch up with Car A? Express the time in terms of given quantities.

Part B: How far from Car B's starting line will the cars be when Car B passes Car A? Express your answer in terms of known quantities.

Answer: Part A: $t=\frac{D_{A}}{v_{B}-v_{A}}$

Part B: $x_{B}=\frac{v_{B}D_{A}}{v_{B}-v_{A}}$

Explanation: First, let's write an equation of motion for each car.

Both cars travels with constant speed. So, they are an uniform rectilinear motion and its position equation is of the form:

$x=x_{0}+vt$

where

$x_{0}$ is initial position

v is velocity

t is time

Car A started the race at a distance. So at t = 0, initial position is $D_{A}$ .

The equation will be:

$x_{A}=D_{A}+v_{A}t$

Car B started at the starting line. So, its equation is

$x_{B}=v_{B}t$

Part A: When they meet, both car are at "the same position":

$D_{A}+v_{A}t=v_{B}t$

$v_{B}t-v_{A}t=D_{A}$

$t(v_{B}-v_{A})=D_{A}$

$t=\frac{D_{A}}{v_{B}-v_{A}}$

Car B meet with Car A after $t=\frac{D_{A}}{v_{B}-v_{A}}$ units of time.

Part B: With the meeting time, we can determine the position they will be:

$x_{B}=v_{B}(\frac{D_{A}}{v_{B}-v_{A}} )$

$x_{B}=\frac{v_{B}D_{A}}{v_{B}-v_{A}}$

Since Car B started at the starting line, the distance Car B will be when it passes Car A is $x_{B}=\frac{v_{B}D_{A}}{v_{B}-v_{A}}$ units of distance.

5 0

3 years ago

The small piston of a hydraulic lift has a cross-sectional of 3 00 cm2 and its large piston has a cross-sectional area of 200 cm

Nesterboy [21]

Q: The small piston of a hydraulic lift has a cross-sectional of 3.00 cm2 and its large piston has a cross-sectional area of 200 cm2. What downward force of magnitude must be applied to the small piston for the lift to raise a load whose weight is Fg = 15.0 kN?

Answer:

225 N

Explanation:

From Pascal's principle,

F/A = f/a ...................... Equation 1

Where F = Force exerted on the larger piston, f = force applied to the smaller piston, A = cross sectional area of the larger piston, a = cross sectional area of the smaller piston.

Making f the subject of the equation,

f = F(a)/A ..................... Equation 2

Given: F = 15.0 kN = 15000 N, A = 200 cm², a = 3.00 cm².

Substituting into equation 2

f = 15000(3/200)

f = 225 N.

Hence the downward force that must be applied to small piston = 225 N

8 0

3 years ago

As an interstellar cloud of hydrogen gas shrinks in size, its rate of rotation

FinnZ [79.3K]

Answer:

INCREASES, BECAUSE ITS ANGULAR MOMENTUM IS CONSERVED.

Explanation: Interstellar cloud of Hydrogen is an accumulation of Hydrogen gas in the cloud.

As the Interstellar cloud of Hydrogen shrinks (reduces) in size,the rate of rotation of the shrinked Interstellar cloud Increases because its angular momentum is conserved. GASEOUS MOLECULES MAKE UP ABOUT 99% OF THE INTERSTELLAR CLOUD WITH HYDROGEN HAVING ABOUT 90% OF THE VOLUME OF GASES IN THE INTERSTELLAR CLOUD.

4 0

3 years ago

Which two possible explanations does the video give for why white light changes into colored light? Color is an impurity added t

Alex777 [14]

Answer:

White light contains seven colors, which are separated by the prism.

White light reacts with chemicals in the air to produce seven colors.

Explanation:

It was first observed by Sir Issac Newton, that when white light is passed through a prism, an elongated, coloured patch of light is obtained on a screen placed behind the prism. The seven colours obtained constitute the spectrum of white light.

In nature, white light is separated into its constituent wavelengths when white light interacts with substances in the atmosphere.

3 0

3 years ago

Tom rides his motorcycle at a speed of 15 meters/second for an hour.

Dahasolnce [82]

Answer:

1 hour to ride his motorcycle

4 0

2 years ago