a car is moving with a constant speed of 20 meters per second.What total distance does the car travel in 2 minutes

Find the average velocity for the time interval beginning when t = 4 with duration 1 seconds, 0.5 seconds, and 0.05 seconds.

s344n2d4d5 [400]

This question is incomplete, the complete question is;

A student dropped a textbook from the top floor of his dorm and it fell according to the formula s(t) = -16t² + 8√t, where t is the time in seconds and s(t) is the distance in feet from the top of the building.

(a) Write a formula for the average velocity of the ball for t near 4.

(b) Find the average velocity for the time interval beginning when t = 4 with duration 1 seconds, 0.5 seconds, and 0.05 seconds

(c) What is your estimate for the instantaneous velocity of the ball at t = 4

Answer:

a)

Average velocity, (Vavg) of the ball for t near 4.

Vavg = [s(4) - s(0)] / (4 - 0)

Where s(4) = -16 × 4² + 8 × √4= - 240 m

s(0) = -16 × 0 + 8 * 0 = 0

b)

duration = 1 sec

Vavg = [s(5) - s(4)] / (5 - 4)

s(5) = -16 × 52 + 8 × √5 = - 382 m

s(4) = -16 × 42 + 8 √4 = - 240 m

Vavg = (-382 - (-240)) / (5 - 4)

Vavg = - 142.1 m/s

duration = 0.5 sec

Vavg = [s(4.5) - s(4)] / (4.5 - 4)

s(4.5) = -16 × 4.52 + 8 × √4.5 = - 307 m

s(4) = -16 × 42 + 8 × √4 = - 240 m

Vavg = (-307 - (-240)) / (4.5 - 4)

Vavg= - 134.1 m/s

duration = 0.05 sec

Vavg = [s(4.05) - s(4)] / (4.05 - 4)

s(4.05) = -16 × 4.052 + 8 × √4.05 = - 246 m

s(4) = -16 × 42 + 8 × √4 = - 240 m

Vavg = (-246 - (-240)) / (4.05 - 4)

Vavg= - 126.8 m/s

c)

Instantaneous velocity, v = ds/dt

= - 16 × 2 × t + 8 ×× (0.5 / √t )

= - 32 × t + 4/√t

ds/dt at t = 4 is,

v = - 32 × 4 + 4 / √4

= - 126 m/s

5 0

3 years ago

Yosef is playing with different kinds of rubber bands. Some are very narrow and some are quite wide. Yosef is curious about the

kari74 [83]

Answer:

He could have many different hypothesis, but here is one.

Explanation:

If rubber bands are wider, then the rubber bands will stretch further, because the wider a rubber band is the stronger it is.

4 0

2 years ago

Read 2 more answers

a ball of mass 0.80 kg moving at a speed of 2.5 m/s along a straight line collided with a mass 2.5 kg which was initially statio

Likurg_2 [28]

The speed of the 0.8 kg ball immediately after collision is 0.625 m/s in opposite direction to the stationary ball.

The given parameters;

mass of the ball, m₁ = 0.8 kg
speed of the ball, u₁ = 2.5 m/s
mass of the object at rest, m₂ = 2.5 kg
final velocity of the object at rest, v₂ = 1 m/s

Let the final velocity of the 0.8 kg ball immediately after collision = v₁

Apply the principle of conservation of linear momentum;

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(0.8 x 2.5) + (2.5 x 0) = (0.8)v₁ + 2.5(1)

2 = 2.5 + (0.8)v₁

-0.5 = (0.8)v₁

$v_1 = \frac{-0.5}{0.8} \\\\v_1 = -0.625 \ m/s$

Thus, the speed of the 0.8 kg ball immediately after collision is 0.625 m/s in opposite direction to the stationary ball.

Learn more here: brainly.com/question/7694106

5 0

2 years ago

All life that we know of is based on carbon. Carbon's ability to form many chemical bonds is an important characteristic that al

AlladinOne [14]

One answer I think would be Oxygen

5 0

3 years ago

A 0.547 kg pizza is thrown straight up in the air. At a height of 2.30 m above the surface of the earth it has a speed of 5.00 m

natima [27]

Answer:

The total mechanical energy of the pizza crust is 19.2 J.

Explanation:

Mechanical energy is that which a body or a system obtains as a result of the speed of its movement or its specific position, and which is capable of producing mechanical work. Then:

Potential energy + kinetic energy = total mechanical energy

Kinetic energy is a form of energy. It is defined as the energy associated with bodies that are in motion and this energy depends on the mass and speed of the body.

Kinetic energy is defined as the amount of work necessary to accelerate a body of a certain mass and in a position of rest, until it reaches a certain speed.

Kinetic energy is represented by the following formula:

Ec = ½ *m*v²

Where Ec is kinetic energy, which is measured in Joules (J), m is mass measured in kilograms (kg), and v is velocity measured in meters over seconds (m / s).

In this case:

m=0.547 kg
v= 5 m/s

Replacing:

Ec = ½ *0.547 kg*(5 m/s)²

and solving you get:

Ec= 6.8375 J

On the other hand, potential energy is the energy that measures the ability of a system to perform work based on its position. In other words, this is the energy that a body has at a certain height above the ground.

Gravitational potential energy is the energy associated with the gravitational force. This will depend on the relative height of an object to some reference point, the mass, and the force of gravity. Then for an object with mass m, at height h, the expression applied to the gravitational energy of the object is:

Ep = m*g*h

Where Ep is the potential energy in joules (J), m is the mass in kilograms (kg) is h the height in meters (m) and g is the acceleration of fall in m / s² (approximately 9.81 m/s²)

In this case:

m= 0.547 kg
g= 9.81 m/s²
h= 2.30 m

Replacing

Ep= 0.547 kg *9.81 m/s²* 2.30 m

and solving you get:

Ep= 12.342 J

So:

Total mechanical energy= 12.342 J + 6.8375 J

Total mechanical energy= 19.1795 J≅ 19.2 J

<u><em>The total mechanical energy of the pizza crust is 19.2 J.</em></u>

6 0

3 years ago