Answer : The number of half-life periods will be, 3
Explanation : Given,
Initial amount of lead = 10 kg
Amount of lead after decay = 1.25 kg
Half-life = 22 years
Formula used :

where,
a = amount of reactant left after n-half lives
= Initial amount of the reactant
n = number of half lives
= half-life
Now put all the given values in the above formula, we get:




Thus, the number of half-life periods will be, 3
Well, since the question GIVES you the initial velocity, the acceleration, and the time, and ASKS for the final velocity, you'd be smart to find an equation that USES the initial velocity, the acceleration, and the time, and FINDS the final velocity.
Have a look at equation B ..... vf = vi + a*t . That's pretty durn close !
vf = (initial velocity) + (acceleration)*(time)
vf = (3 m/s) + (5 m/s²)*(4 sec)
vf = (3 m/s) + (20 m/s)
vf = 23 m/s
Answer:
A. 33.77 m/s
B. 6.20 s
Explanation:
Frame of reference:
Gravity g=-9.8 m/s^2; Initial position (roof) y=0; Final Position street y= -21 m
Initial velocity upwards v= 27 m/s
Part A. Using kinematics expression for velocities and distance:

Part B. Using Kinematics expression for distance, time and initial velocity

Since it is a second order equation for time, we solved it with a calculator. We pick the positive solution.
b.
Newton's second law of motion can be formally stated as follows: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
https://www.grc.nasa.gov/www/k-12/airplane/newton2.html
To solve this problem we will apply the concept of rotational kinetic energy. Once this energy is found we will proceed to find the time from the definition of the power, which indicates the change of energy over time. Let's start with the kinetic energy of the rotating flywheel is

Here
I = moment of inertia
Angular velocity
Here we have that,


Replacing the value of the moment of inertia for this object we have,



The expression for average power is




Therefore the correct answer is 620s.