A 500 kg elevator starts from rest. It moves upward for 4.00 s with constant acceleration until it reaches its cruising speed, 1.75 m/s.

(a) What is the average power of the elevator motor during this period?

(b) How does this power compare with the motor power when the elevator moves at its cruising speed?

work:

acceleration = velocity/time = 1.75/4 = .4375
distance = .5*acceleration*t^2 = .5*.4375*16 = 3.5
energy = mass*gravity*distance + (mass/2)*v^2
=500*9.8*3.5+(500/2)*(1.75)^2
=17150.0+765.625 = 17915.625
power = work/time = 17915.625/4 = 4478.9063
answer for part a) 4478.9063

do not know how to do part b) could not figure out for myself

To find the average power of the elevator motor, we can use the formula:

Average Power = Work / Time

Let's break down the problem into smaller steps to find the answer.

Step 1: Find the distance covered by the elevator during the acceleration phase.
We can use the equation of motion to find the distance covered during the initial 4.00 seconds when the elevator is accelerating.

The equation of motion is:
s = ut + (1/2)at^2,
where s is the distance, u is the initial velocity, t is the time, and a is the acceleration.

Given:
Initial velocity, u = 0 m/s (elevator starts from rest)
Time, t = 4.00 s
Acceleration, a = ?

Rearranging the equation:
s = (1/2)at^2

Since we need to find the acceleration, we can rearrange the equation as:
a = 2s / t^2

Substituting the values:
s = distance covered during acceleration phase = ?
t = 4.00 s

Step 2: Find the acceleration.
Given:
Mass, m = 500 kg

We can use Newton's second law to find the acceleration.
F = ma,
where F is the force and m is the mass.

The force causing the acceleration is the weight of the elevator, which is given by:
W = mg,
where g is the acceleration due to gravity.

Substituting the values:
m = 500 kg
g = 9.8 m/s^2

W = mg = 500 kg x 9.8 m/s^2

Step 3: Calculate the force causing acceleration.
We know that force is the product of mass and acceleration.
F = ma,
where F is the force, m is the mass, and a is the acceleration.

Given:
m = 500 kg
a = acceleration = ?

Substituting the values:
F = ma = (500 kg) x (acceleration)

Since we already know the weight W = mg = (500 kg) x (9.8 m/s^2), we can equate this weight to the force causing acceleration:
W = F

Step 4: Calculate the distance covered during the acceleration phase.
Using the value of force (F) obtained in Step 3 and the equation of motion (s = (1/2)at^2) calculated in Step 1, we can find the distance covered during the acceleration phase.

Substituting the values:
s = (1/2)at^2 = (1/2)(F/m)t^2

Step 5: Calculate the work done during the acceleration phase.
Work is given by the equation:
Work = force x distance,
where force is the force causing acceleration and distance is the distance covered during the acceleration phase.

Given:
Force, F = ?
Distance, s = ?

Substituting the values:
Work = Force x Distance = F x s

Step 6: Calculate the average power.
Finally, to find the average power during the acceleration phase, we can use the equation:
Average Power = Work / Time

Given:
Work = ?
Time = 4.00 s

Substituting the values:
Average Power = Work / Time

You can follow these steps to find the answer to part (a) of the question. To answer part (b), you need to compare the average power calculated in part (a) with the motor power when the elevator moves at its cruising speed, 1.75 m/s.