<span> We're given that x=25 when t=2: </span>
<span>25 = 3 + 12(2) + (1/2)a(2)^2 </span>
<span>Thus a = -1 cm/sec^2</span>
Explanation :
The forces acting on hot- air balloon are:
Weight, (W)
Force due to air resistance, (F)
Upthrust force, (U)
Its weight W is acting in downward direction. The upthrust force U acts in upward direction. When the balloon is moving upward, the air resistance is in downward and vice versa.
In this case, the hot-air balloon descends vertically at constant speed.
so, 
and 
so,
....................(1)
when it is ascending let the weight that it is releasing is R, so
..........(2)
solving equation (1) and (2)

2F is the weight of material that must be released from the balloon so that it ascends vertically at the same constant speed.
Explanation:
Given that,
Mass if the rock, m = 1 kg
It is suspended from the tip of a horizontal meter stick at the 0-cm mark so that the meter stick barely balances like a seesaw when its fulcrum is at the 12.5-cm mark.
We need to find the mass of the meter stick. The force acting by the stone is
F = 1 × 9.8 = 9.8 N
Let W be the weight of the meter stick. If the net torque is zero on the stick then the stick does not move and it remains in equilibrium condition. So, taking torque about the pivot.

W = 3.266 N
The mass of the meters stick is :

So, the mass of the meter stick is 0.333 kg.
Answer:
Correct answer: 11. Total distance d = 200m ; 12. Vav = 3.63m/s ;
13. Total displacement Dt = 0m ; 14. V₂(10s-15s) = 0 m/s ;
15. V₃(15s-40s) = 4 m/s ; 16. V₁(0s-10s) = 6 m/s > V₄(40s-55s) = 2.67 m/s
Explanation:
The whole movement can be divided into four stages.
In the first stage the subject moves 60m in a positive direction for 10s,
in the other it is stationary for 5s, in the third it moves 100m in the opposite (negative) direction for 25s and in the fourth in the positive 40m for 15s.
11. Total distance = 60 + 0 + 100 + 40 = 200m
12. The formula for calculating the average speed (velocity) is
Vav = (S₁ + S₂ + S₃ + S₄) / (t₁ + t₂ + t₃ + t₄)
Vav = (60 + 0 + 100 + 40)/ (10 + 5 + 25 + 15) = 200/55 = 3.63 m/s
13. The movement started from the origin and ended at the origin
Total displacement is zero meters.
14. The speed between 10s and 15s is zero, because he did not move.
15. V₃ = S₃/t₃ = 100/25 = 4 m/s
16. V₁ = S₁/t₁ = 60/10 = 6 m/s and V₄ = S₄/t₄ = 40/15 = 2.67 m/s
V₁ > V₄
God is with you!!!