Answer:
Solution:
we have given the equation of motion is x(t)=8sint [where t in seconds and x in centimeter]
Position, velocity and acceleration are all based on the equation of motion.
The equation represents the position. The first derivative gives the velocity and the 2nd derivative gives the acceleration.
x(t)=8sint
x'(t)=8cost
x"(t)=-8sint
now at time t=2pi/3,
position, x(t)=8sin(2pi/3)=4*squart(3)cm.
velocity, x'(t)=8cos(2pi/3)==4cm/s
acceleration, x"(t)==8sin(2pi/3)=-4cm/s^2
so at present the direction is in y-axis.
Answer:
3.28 cm
Explanation:
To solve this problem, you need to know that a magnetic field B perpendicular to the movement of a proton that moves at a velocity v will cause a Force F experimented by the particle that is orthogonal to both the velocity and the magnetic Field. When a particle experiments a Force orthogonal to its velocity, the path it will follow will be circular. The radius of said circle can be calculated using the expression:
r = 
Where m is the mass of the particle, v is its velocity, q is its charge and B is the magnitude of the magnetic field.
The mass and charge of a proton are:
m = 1.67 * 10^-27 kg
q = 1.6 * 10^-19 C
So, we get that the radius r will be:
r =
= 0.0328 m, or 3.28 cm.
Heat required to change the phase of ice is given by
Q = m* L
here
m = mass of ice
L = latent heat of fusion
now we have
m = 45 kg
L = 334 KJ/kg
now by using above formula


In KJ we can convert this as

so the correct answer is D option
As an object falls from rest, its gravitational energy is converted to kinetic energy
G.P.E = K.E = mgh
K.E = (80 Kg)(9.8 m/s²)(30 m)
K.E. = 23,520 J
We know, R = V / I
Here, V = 86 V
I = 3 A
Substitute their values,
R = 86 / 3
R = 28.67 Ohm
In short, Your Answer would be 28.67 Ohms
Hope this helps!