Answer:
false statement : b ) For the motion of a cart on an incline plane having a coefficient of kinetic friction of 0.5, the magnitude of the change in kinetic energy equals the magnitude of the change in gravitational potential energy
Explanation:
mechanical energy = potential energy + kinetic energy = constant
differentiating both side
Δ potential energy + Δ kinetic energy = 0
Δ potential energy = - Δ kinetic energy
first statement is true.
Friction is a non conservative force so inter-conversion of potential and kinetic energy is not possible in that case. In case of second option, the correct relation is as follows
change in gravitational potential energy = change in kinetic energy + work done against friction .
So given 2 nd option is incorrect.
In case of no change in gravitational energy , work done is equal to
change in kinetic energy.
Net force would be towards the right and back (opposite direction of motion) since it's slowing down (decelerating) and turning right.
Answer:
(a) A = m/s^3, B = m/s.
(b) dx/dt = m/s.
Explanation:
(a)

Therefore, the dimension of A is m/s^3, and of B is m/s in order to satisfy the above equation.
(b) 
This makes sense, because the position function has a unit of 'm'. The derivative of the position function is velocity, and its unit is m/s.
Answer:
525 Bq
Explanation:
The decay rate is directly proportional to the amount of radioisotope, so we can use the half-life equation:
A = A₀ (½)^(t / T)
A is the final amount
A₀ is the initial amount,
t is the time,
T is the half life
A = (8400 Bq) (½)^(18.0 min / 4.50 min)
A = (8400 Bq) (½)^4
A = (8400 Bq) (1/16)
A = 525 Bq
Answer: Tension = 47.8N, Δx = 11.5×
m.
Tension = 95.6N, Δx = 15.4×
m
Explanation: A speed of wave on a string under a tension force can be calculated as:

is tension force (N)
μ is linear density (kg/m)
Determining velocity:


0.0935 m/s
The displacement a pulse traveled in 1.23ms:


Δx = 11.5×
With tension of 47.8N, a pulse will travel Δx = 11.5×
m.
Doubling Tension:



|v| = 0.1252 m/s
Displacement for same time:


15.4×
With doubled tension, it travels
15.4×
m