Answer:
(A) 60 J
Explanation:
At state 1
KE₁=100 J
At state 2
KE₂ = 0
U₂=80 J
Given that surface is rough so friction force will act in opposite to the direction of motion
Lets take work done by friction = Wfr
From work power energy
Work done by all forces = Change in kinetic energy
Wfr + U₂=ΔKE
Wfr+80 = 100
Wfr= 20 J
Now when book slides from top position then
Wfr+ U = KEf - KEi
-20 + 80 = KEf-0
KEf= 60 J
(A) 60 J
The displacement vector (SI units) is
![\vec{r} =At\hat{i}+A[t^{3}-6t^{2}]\hat{j}](https://tex.z-dn.net/?f=%5Cvec%7Br%7D%20%3DAt%5Chat%7Bi%7D%2BA%5Bt%5E%7B3%7D-6t%5E%7B2%7D%5D%5Chat%7Bj%7D)
The speed is a scalar quantity. Its magnitude is

Answer: At√(t⁴ - 12t³ + 36t² + 1)
This problem here is an example of inelastic collision where kinetic energy is not conserved but momentum is. We calculate as follows:
m1v1 + m2v2 = (m1 + m2)v3
v3 = m1v1 + m2v2 / m1 + m2
v3 = (30.2)(1000) + (5000)(0) / (30.2 + 5000)
v3 = 6.00 m/s