1st derivative gives velocity;
d r(t)/ dt = 2t i + 6 j + 4/t k
2nd derivative gives acceleration;
d^2 r(t)/ dt^2 = 2 i - 4/ t^2
Speed ;
Square root of (4 t^2 + 36 + 16/ t^2)
For a given time, like 2 seconds, t will be 2. And answer of speed will be scalar.
Answer:
P = 5sin(880πt)
Explanation:
We write the pressure in the form P = Asin2πft where A = amplitude of pressure, f = frequency of vibration and t = time.
Now, striking the middle-A tuning fork with a force that produces a maximum pressure of 5 pascals implies A = 5 Pa.
Also, the frequency of vibration is 440 hertz. So, f = 440Hz
Thus, P = Asin2πft
P = 5sin2π(440)t
P = 5sin(880πt)
Answer:
Explanation:
We have to find electric potential V at a distance r.
a) For r>R,
The electric field in the cylinder is given by
E.A equating it to the other electric field given by
б.A/ε₀
Here the area of cylinder is given by= 2*3.14*r*L
While for the outside, the area= 2*3.14*R*L
Equating both, we get
E= бR/rε₀
Now,
The potential difference is given as:
ΔV= -бR/rε₀ and integrating right side with respect to dr under limits r and R.
Where ΔV= V₀-V
So solving we get
V₀=V-бR/ε₀ln (r/R)
b) For r<R i.e. inside the cylinder
There will be no electric field produced as E=0
So ultimately Vin= V
c) V=0 at r= infinity.
<span>Science is orderly knowledge proven by experimentations.</span>
