It's true, when we lift an object we add energy to it.
because, when we lift an object by applying force , the object attains a height and hence the energy gets stored in it, in the form gravitational potential energy .
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.
Complete question:
What is the peak emf generated by a 0.250 m radius, 500-turn coil is rotated one-fourth of a revolution in 4.17 ms, originally having its plane perpendicular to a uniform magnetic field 0.425 T. (This is 60 rev/s.)
Answer:
The peak emf generated by the coil is 15.721 kV
Explanation:
Given;
Radius of coil, r = 0.250 m
Number of turns, N = 500-turn
time of revolution, t = 4.17 ms = 4.17 x 10⁻³ s
magnetic field strength, B = 0.425 T
Induced peak emf = NABω
where;
A is the area of the coil
A = πr²
ω is angular velocity
ω = π/2t = (π) /(2 x 4.17 x 10⁻³) = 376.738 rad/s = 60 rev/s
Induced peak emf = NABω
= 500 x (π x 0.25²) x 0.425 x 376.738
= 15721.16 V
= 15.721 kV
Therefore, the peak emf generated by the coil is 15.721 kV
