Answer:
Although this question is not complete, I would give a general solution to this kind of problems.
If y(t) describes the position of a body with time such that
y(t) = at^(n) + bt^(m) + C
Then
V(t) = dy(t)/dt = ant^(n-1) + bmt^(m-1)
Explanation:
As an example supplies the position of a particle is given by
y(t) = 4t³- 3t² + 9
V(t) = 4x3t²- 3x2t¹
V(t) = d(t)/dt = 12t² - 6t.
Another example,
If y(t) = 15t³ - 2t² + 30t -80
V(t) = d(t)/dt = 15x3t² - 4t +30 = 45t² + 4t + 30.
Basically, in the equations above the powers of t reduces by one when computing the velocity function from y(t) by differentiation (calculating the derivative of y(t)). The constant term C (9 and 80 in the functions of y(t) in examples 1and 2 above) reduces to zero because the derivative of a constant (and ordinary number without the t attached to it) is always zero.
One last example,
y(t) = 2t^6 -3t²
V(t) = d(t)/dt = 12t^5 - 6t
Answer:
Explanation:
It is given that,
Distance between the spotlight and the wall, y = 24 m
Height of the woman, h = 2 m
The woman walks toward the building at the rate of 0.6 m/s, 
In the attached figure, triangle ABC and MNC are similar. So,
............(1)
When she is 2 meters from the building. So x = 24-2 = 22 m
Differentiating equation (1) i.e.
So, her shadow is decreasing at the rate of 0.059 m/s. Hence, this is the required solution.
Answer:
Explanation:
We know that for a capacitor 
, where <em>Q </em>is the charge of one plate, <em>C</em> the capacitance and <em>V</em> the potential between the plates.
We also know that 
, since 
is the surface charge density and <em>A</em> the area of the plate (both equal in our case).
Putting all together:
Which for our values is:
Where we notice that the S.I. units combination FV/C must not have units (we can verify it directly from their definitions or we notice that 
is enough to describe an area).
Work done = Mass * displacement
W = 50 * 5 = 250 watts
In short, Your Answer would be 250 watts
Hope this helps!
<span>Forecasting the time of, location, and magnitude of a seismic event does not prevent
the event from happening, but it can help us reduce the destruction caused by
A) earthquakes.</span>
