The kinetic energy of a moving object is given by

where m is the object's mass and v its velocity.
In our problem, the initial kinetic energy is:

while the final kinetic energy is:

So, the kinetic energy lost by Lucy and her bike is
Answer:
c.
=0 and 
Explanation:
We are given that two particles collide and stick together.
If there is no external force act on the two particles then ,it is inelastic collision.
Inelastic collision: There is some loss of kinetic energy but the momentum is conserved.
According to law of conservation of momentum
Initial momentum=Final momentum
Change in momentum=Final momentum-Initial momentum=0
Change in momentum=
Initial kinetic energy is greater than final kinetic energy.
Change in kinetic energy=Final kinetic energy-kinetic energy=- negative

Hence, option c is true.
c.
=0 and 
Answer:
The magnitude of the torque on the loop due to the magnetic field is
.
Explanation:
Given that,
Diameter = 10 cm
Current = 0.20 A
Magnetic field = 0.30 T
Unit vector
We need to calculate the torque on the loop
Using formula of torque

Where, N = number of turns
A = area
I = current
B = magnetic field
Put the value into the formula


Hence, The magnitude of the torque on the loop due to the magnetic field is
.
Answer:
K = 1.525 10⁻⁹ x⁴ + 4.1 10⁶ x
Explanation:
To find the variation of kinetic energy, let's use the work energy theorem
W = ΔK
∫ F .dx = K -K₀
If the body starts from rest K₀ = 0
∫ F dx cos θ = K
Since the force and displacement are in the same direction, the angle is zero, so the cosine is 1
we substitute and integrate
α ∫ x³ dx + β ∫ dx = K
α x⁴ / 4 + β x / 1 = K
we evaluate from the lower limit F = 0 to the upper limit F
α (x⁴ / 4 -0) + β (x -0) = K
K = αX⁴ / 4 + β x
K = 1.525 10⁻⁹ x⁴ + 4.1 10⁶ x
in order to finish the calculation we must know the displacement