1) The average velocity is 
2) The instantaneous velocity is 
Explanation:
1)
The average velocity of an object is given by
where
d is the displacement
t is the time elapsed
In this problem, the position of the particle is given by the function
where t is the time.
The position of the particle at time t = 6 sec is
While the position at time t = 12 sec is
So, the displacement is
And therefore the average velocity is
2)
The instantaneous velocity of a particle is given by the derivative of the position vector.
The position vector is
By differentiating with respect to t, we find the velocity vector:
Therefore, the instantaaneous velocity at any time t can be found by substituting the value of t in this expression.
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Answer:
B) Power
Explanation:
The power is defined by the following equation:
P = W / t
where:
W = work = Force * Distance = [Newton] * [meter]
t = time = seconds
The units for work are give en Newton per second, which is equal to Joules
And for power the unit used commonly is Watts, therefore:
Watts = (Joule/second)
During the phase transition vapour --> liquid water, the temperature of the water does not change; the molecules of water release heat and the amounf of heat released is equal to
where
m is the mass of the water
is the latent heat of evaporation.
For water, the latent heat of evaporation is
, while the mass of the water is
so, the amount of heat released in the process is
Answer:
Decreases to half.
Explanation:
From the question given above, the following data were obtained:
Initial mass (m₁) = m
Initial force (F₁) = F
Initial acceleration (a₁) =?
Final mass (m₂) = ½m
Final force (F₂) = ¼F
Final acceleration (a₂) =?
Next, we shall determine a₁. This can be obtained as follow:
F₁ = m₁a₁
F = ma₁
Divide both side by m
a₁ = F / m
Next, we shall determine a₂.
F₂ = m₂a₂
¼F = ½ma₂
2F = 4ma₂
Divide both side by 4m
a₂ = 2F / 4m
a₂ = F / 2m
Finally, we shall determine the ratio of a₂ to a₁. This can be obtained as follow:
a₁ = F / m
a₂ = F / 2m
a₂ : a₁ = a₂ / a₁
a₂ / a₁ = F/2m ÷ F/m
a₂ / a₁ = F/2m × m/F
a₂ / a₁ = ½
Cross multiply
a₂ = ½a₁
From the illustrations made above, the acceleration of the car will decrease to half the original acceleration
The energy used by the light bulb in half an hour is 180000 J and the amount of thermal energy generated is 158400 J.
What is Energy?
Energy is the ability or the capacity to do work.
To calculate the energy of the light bulb we use the formula below
Formula:
- E = Pt.......... Equation 1
Where:
- E = Energy used by the bulb in a half-hour
- P = Power of the bulb
- t = Time
Given:
- P = 100 W
- t = 1/2 hour = 30 minutes = (30×60) = 1800 seconds
Substitute these values into equation 1
- E = (100×1800)
- E = 180000 J
- If the light converts 12% of electric energy to light energy, then 88% of the energy is used to generate thermal energy
Therefore,
- Thermal energy = (180000×88/100) = 158400 J
Hence, the energy used by the light bulb in half an hour is 180000 J and the amount of thermal energy generated is 158400 J.
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