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3 years ago

The velocity of an object is v(t) = 27 − t2, 0 ≤ t ≤ 6 where v is measured in meters per second and t is the time in seconds.

Physics

1 answer:

arlik [135]3 years ago

8 0

Answer:

(a) 23 m/s, -4 m/s²

(b) Speed is decreasing.

Explanation:

The velocity of the object is given as:

v(t) = 27 - t²

When t = 2 secs, velocity, v(2) becomes:

v(2) = 27 - (2)²

v(2) = 27 - 4

v(2) = 23 m/s

The acceleration is the first derivative of the velocity, dv/dt:

a(t) = dv(t)/dt = -2t

Acceleration after 2 secs, a(2) is:

a(2) = -2*2

a(2) = -4 m/s²

(b) When velocity and acceleration have opposite signs, it means that the velocity and acceleration are in opposite directions, hence, the object is slowing down.

In other words, the speed is decreasing.

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A well-insulated bucket of negligible heat capacity contains 129 g of ice at 0°C.

Luba_88 [7]

Answer:

The final equilibrium temperature of the system is $T = 12.48^oC$

For the ice it would melt completely the mass that would remain is Zero

Explanation:

In the following question we are provided with

Mass of the ice $M_{i}$ = 129 g = 0.129 kg

Mass of the steam $M_s$ = 19 g = 0.019 kg

Initial temperature is $T_i$ = 0°C

Temperature of steam $T_s$ = 100°C

Following the change of state of water in the question

The energy required by ice to change to water is mathematically given as

$Q_A = M_iL_f$

Where $L_f$ is a constant known as heat of fusion and the value is $334*10^3 J/kg$

$Q_A = 0.129 *334 *10^3 = 43086 J$

The energy been released when the steam changes to water is mathematically given as

$Q_B = M_s * L_v$

Where $L_v$ is a constant known as heat of vaporization and the value is $2256*10^3J/kg$

$Q_B = 0.019 * 2256*10^3 = 42864J$

The energy released when the temperature of water decrease from 100°C to 0°C is

$Q_C = M_s *C_water ($ 100°C)

Where $C_{water}$ is the specific heat of water which has a value $4186J/kg \cdot K$

$Q_C = 0.019 *4186*100 = 7953.4$

Looking at the values we obtained we noticed that ]

$Q_B + Q_C > Q_A$

What this means is that the ice will melt

bearing in mind the conservation of energy

looking the way at which water at different temperature were mixed according to the question

Heat lossed by the vapor = heat gained by ice

$Q_B + M_s *C_{water}(100-T) = Q_A + M_i C_{water} T$

$T = \frac{Q_B+M_s *C_{water}(100^oC)-Q_A}{(M_s *C_{water})+(M_i*C_{water})}$

$T = \frac{42864+7953.4-43086}{(0.019+0.129)(4186)}$

$T = 12.48^oC$

3 0

3 years ago

in the primitive yo-yo apparatus (figure 1), you replace the solid cylinder with a hollow cylinder of mass m , outer radius r ,

kirza4 [7]

The magnitude of the downward acceleration of the hollow cylinder is 6m/s^2.

Z = I α

T.R =1/2 M ( $R^{2}$ + $(R/2)^{2}$ )α

T.R = 1/2M 5 $R^{2}$ /4 α

T = 5Ma/8

Mg - T = Ma

Mg - 5Ma/8 = Ma

Mg= 5Ma/8 + Ma = 13Ma / 8

acceleration = 8g/13 = 6 m/s^2

The rate at which an object's velocity with respect to time changes is called its acceleration. The direction of the net force imposed on an item determines its acceleration in relation to that force. According to Newton's Second Law, the magnitude of an object's acceleration is the result of two factors working together

The size of the net balance of all external forces acting on that item is directly proportional to the magnitude of this net resultant force; the magnitude of that object's mass, depending on the materials from which it is built, is inversely related to its mass.

Learn more about acceleration here:

brainly.com/question/2303856

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1 year ago

Technician A says the manual lever position (MLP) switch is sometimes called a transmission range switch or a neutral safety swi

Phantasy [73]

Answer:

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During low-intensity activity, your body obtains most of its energy from

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Carbohydrates, in cellular respiration.

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