Answer:
(a) Time t = 16.46 sec
(b) Time t =13.466 sec
(c) Deceleration = 
Explanation:
(a) As the train starts from rest its initial velocity u = 0 m/sec
Acceleration 
Final speed v = 80 km/hr

From first equation of motion v =u+at
So 
(b) Now initial speed u = 22.22 m/sec
As finally train comes to rest so final speed v=0 m/sec
Deceleration 
So 
(c) We have given that initial velocity = 80 km/hr = 22.22 m/sec
Final velocity v = 0 m/sec
Time t = 8.30 sec
So acceleration is given by

As acceleration is negative so it is a deceleration
I used to wish that I can fly
Answer: D(t) = 
Explanation: A harmonic motion of a spring can be modeled by a sinusoidal function, which, in general, is of the form:
y =
or y = 
where:
|a| is initil displacement
is period
For a Damped Harmonic Motion, i.e., when the spring doesn't bounce up and down forever, equations for displacement is:
or 
For this question in particular, initial displacement is maximum at 8cm, so it is used the cosine function:
period =
12 =
ω = 
Replacing values:

The equation of displacement, D(t), of a spring with damping factor is
.
Answer:
F = 104.832 N
Explanation:
given,
upward acceleration of the lift = 1.90 m/s²
mass of box containing new computer = 28 kg.
coefficient of friction = 0.32
magnitude of force = ?
box is moving at constant speed hence acceleration will be zero.
Now force acting due to lift moving upward =
F = μ m ( g + a )
F = 0.32 × 28 × ( 9.8 + 1.9 )
F = 104.832 N
hence, the force applied should be equal to 104.832 N