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3 years ago

13

A 1210-kg vehicle is moving along a horizontal surface with a speed of 28.3 m/s. What work (in J) must be done by the brakes to

bring this car to rest in 4.58 seconds

1 answer:

ArbitrLikvidat [17]3 years ago

6 0

Answer:

4.85*10^5 Joules

Explanation:

The work done in bringing the car to rest would be equivalent to the kinetic energy of the vehicle while it is in motion.

The kinetic energy of the vehicle is 1/2mv^2; where m is the mass and v is the velocity.

Work done=1/2*1210*28.3^2

Another approach would be to calculate the force applied and the braking distance of the vehicle and then applying the formula of work done. However, it would've been an unnecessary hassle.

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A ball is thrown straight up. What are the velocity and acceleration of the ball at the highest point in its path?

zubka84 [21]

Answer:

b. v = 0, a = 9.8 m/s² down.

Explanation:

Hi there!

The acceleration of gravity is always directed to the ground (down) and, near the surface of the earth, has a constant value of 9.8 m/s². Since the answer "b" is the only option with an acceleration of 9.8 m/s² directed downwards, that would solve the exercise. But why is the velocity zero at the highest point?

Let´s take a look at the height function:

h(t) = h0 + v0 · t + 1/2 g · t²

Where

h0 = initial height

v0 = initial velocity

t = time

g = acceleration due to gravity

Notice that the function is a negative parabola if we consider downward as negative (in that case "g" would be negative). Then, the function has a maximum (the highest point) at the vertex of the parabola. At the maximum point, the slope of the tangent line to the function is zero, because the tangent line is horizontal at a maximum point. The slope of the tangent line to the function is the rate of change of height with respect to time, i.e, the velocity. Then, the velocity is zero at the maximum height.

Another way to see it (without calculus):

When the ball is going up, the velocity vector points up and the velocity is positive. After reaching the maximum height, the velocity vector points down and is negative (the ball starts to fall). At the maximum height, the velocity vector changed its direction from positive to negative, then at that point, the velocity vector has to be zero.

8 0

4 years ago

Why are ocean currents important?

Lelu [443]

For the considerably longer periods– decades to millennia – which are relevant for climate change, the slightly larger heat capacity of the deep ocean<span> is </span>important. Ocean currents<span> and mixing by winds and waves can transport and redistribute heat to deeper </span>ocean<span> layers.</span>

4 0

3 years ago

A hollow cylinder with an inner radius of and an outer radius of conducts a 3.0-A current flowing parallel to the axis of the cy

Artemon [7]

Complete Question:

A hollow cylinder with an inner radius of 4.0mm and an outer radius of 30mm conducts a 3.0-A current flowing parallel to the axis of the cylinder. If the current density is uniform throughout the wire, what is the magnitude of the magnetic field at a point 12mm from its center?

Answer:

The magnitude of the magnetic field = 7.24 μT

Explanation:

Inner radius, a = 4.0 mm = 0.004 m

Outer radius, b = 30 mm = 0.03 m

Radius, r = 12 mm = 0.012 m

let h² = b² - a²

h² = 0.03² - 0.004²

h² = 0.000884

Let d² = r² - a²

d² = 0.012² - 0.004²

d² = 0.000128

Current I = 3A

μ = 4π * 10⁻⁷

The magnitude of the magnetic field is given by:

$B = \frac{\mu I d^{2} }{2\pi r h^{2} } \\B = \frac{4\pi * 10^{-7} * 3* 0.000128^{2} }{2\pi *0.012* 0.000884^{2} }$

B = 7.24 * 10⁻⁶T

B = 7.24 μT

7 0

3 years ago

Suppose that the inverse market demand for silicone replacement tips for Sony earbud headphones is p = pN - 0.1Q, where p is t

lbvjy [14]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

The effect of a change in the price of a new pair of headphones on the equilibrium price of replacement tips ( dp/dpN) is

$\frac{\delta p}{\delta p_N} =1$

b

The value of Q and p at equilibruim is

$Q_e = 250$ and $p_d =$ 5

The consumer surplus is $C= 3125$

The producer surplus is $P = 375$

Explanation:

From the question we are told that

The inverse market demand is $p_d = p_N -0.1Q$

The inverse supply function is $p_s = 2+ 0.012Q$

a

The effect of change in the price is mathematically given as

$\frac{\delta p}{\delta p_N}$

Now differntiating the inverse market demand function with respect to $p_N$

We get that

$\frac{\delta p}{\delta p_N} =1$

b

We are told that $p_N =$ $30

Therefore the inverse market demand becomes

$p_d = 30 -0.1Q$

At equilibrium

$p_d = p_s$

So we have

$30 -0.1Q_e = 2+ 0.012Q_e$

Where $Q_e$ is the quantity at equilibrium

$28 = 0.112Q_e$

$Q_e = \frac{28}{0.112}$

$Q_e = 250$

Substituting the value of Q into the equation for the inverse market demand function

$p_d = 30 - 0.1 (250 )$

$p_d =$ 5

Looking at the equation for $p_d \ and \ p_s$ we see that

For Q = 0

$p_d = 30$

$p_s =2$

And for Q = 250

$p_d = 5$

$p_s = 5$

Hence the consumer surplus is mathematically evaluated as

$C = \frac{1}{2} * Q_e * (30 -5)$

Substituting value

$C = \frac{1}{2} * 250 (30-5)$

$C= 3125$

And

The producer surplus is mathematically evaluated as

$P = \frac{1}{2} *250 * (5-2)$

$P = 375$

4 0

3 years ago

PLEASE HELPPP IT DUES IN 30 minutes

Nuetrik [128]

Answer:

140m

70sec I cant show my work but I gave you a push

Explanation:

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3 years ago