The average velocity can be calculated using the formula:
v = d / t
For the 1st car, the velocity is calculated
as:
v1 = 8.60 m / 1.80 s = 4.78 m / s
While that of the 2nd car is:
v2 = 8.60 m / 1.66 s = 5.18 m / s
Now we can solve for the acceleration using the formula:
v2^2 = v1^2 + 2 a d
Rewriting in terms of a:
a = (v2^2 – v1^2) / 2 d
a = (5.18^2 – 4.78^2) / (2 * 8.6)
a = 0.23 m/s
Therefore the train has a constant acceleration of about
0.23 meters per second.
Answer:
(a) 
(b) 
(c) K.E. = 21.168 J
(d) 
Explanation:
Given:
- mass of a block, M = 3.6 kg
- initial velocity of the block,

- constant downward acceleration,

That a constant upward acceleration of
is applied in the presence of gravity.
∴
- height through which the block falls, d = 4.2 m
(a)
Force by the cord on the block,



∴Work by the cord on the block,


We take -ve sign because the direction of force and the displacement are opposite to each other.

(b)
Force on the block due to gravity:

∵the gravity is naturally a constant and we cannot change it


∴Work by the gravity on the block,



(c)
Kinetic energy of the block will be equal to the net work done i.e. sum of the two works.
mathematically:


K.E. = 21.168 J
(d)
From the equation of motion:

putting the respective values:

is the speed when the block has fallen 4.2 meters.
Answer:
Thus, the payback time for cavity wall insulation is 7.5 years