Answer:
Explanation:
a net force of F causes a cart with a mass of M to accelerate at 48 cm/s/s.
F = M x 48
Mass M = F / 48
a )
When force = 2F and mass = M
Acceleration = force / mass
= 2F /F/48
= 48 X 2 = 96 cm/s²
b )
When force = F and mass = 2M
Acceleration = force / mass
= F /2F/48
= 24 cm/s²
c )
When force = 2F and mass = 2M
Acceleration = force / mass
= 2F /2F/48
= 48 cm/s
d )
When force = 2F and mass = 4M
Acceleration = force / mass
= 2F /4F/48
= 24 cm/s
e)
When force = 4F and mass = 2M
Acceleration = force / mass
= 4F / 2M
= 4F / 2 F/48
= 48 x 2
Acceleration = 96 cm/s²
Answer:
h'=0.25m/s
Explanation:
In order to solve this problem, we need to start by drawing a diagram of the given situation. (See attached image).
So, the problem talks about an inverted circular cone with a given height and radius. The problem also tells us that water is being pumped into the tank at a rate of
. As you may see, the problem is talking about a rate of volume over time. So we need to relate the volume, with the height of the cone with its radius. This relation is found on the volume of a cone formula:

notie the volume formula has two unknowns or variables, so we need to relate the radius with the height with an equation we can use to rewrite our volume formula in terms of either the radius or the height. Since in this case the problem wants us to find the rate of change over time of the height of the gasoline tank, we will need to rewrite our formula in terms of the height h.
If we take a look at a cross section of the cone, we can see that we can use similar triangles to find the equation we are looking for. When using similar triangles we get:

When solving for r, we get:

so we can substitute this into our volume of a cone formula:

which simplifies to:


So now we can proceed and find the partial derivative over time of each of the sides of the equation, so we get:

Which simplifies to:

So now I can solve the equation for dh/dt (the rate of height over time, the velocity at which height is increasing)
So we get:

Now we can substitute the provided values into our equation. So we get:

so:

Answer:
The value of the constant k is 2
Explanation:
We have the equation of the velocity
= kt² , where k
is constant and t is the time in second
The particle's position at
= 0 is
= -9 m
The particle's position at
= 3 s is
= 9 m
We need to find the value of the constant k
The relation between the velocity and the displacement in a particular
time is x = 
Remember in integration we add power by 1 and divide the expression
by the new power
→ x = 
c is the constant of integration to find it substitute the initial value of x
and t in the equation of x
→
= 0 ,
= -9 m
→ -9 =
k (0)³ + c
→ -9 = c
Substitute the value of c in the equation of x
→ x =
k t³ - 9
To find k substitute the values of
= 3 s ,
= 9 m
→ 9 =
k (3)³ - 9
→ 9 =
(27) k - 9
→ 9 = 9 k - 9
Add 9 to both sides
→ 18 = 9 k
Divide both sides by 9
→ k = 2
<em>The value of the constant k is 2</em>
Answer:
All of the above
Explanation:
Astronomers use all of those measures to classify stars. If you want to look more into classifying stars, check out the Hertzsprung-Russel Diagram. It covers how to identify red giants, main sequence, dwarf stars, ect. Distance from earth is typically measured in light years. The color of stars generally determines how hot they are. (Blue stars are the hottest) Also, the parallax method is used to measure stars that are closer to earth. This method relies heavily on geometry though.
Hope this helped!

Actually Welcome to the Concept of the kinematics of a body.
Since, we know that Velocity = Distance / time
hence, V = 20/5 = 4 m/s
hence the velocity of the RC car is 4 m/s westwards direction.