Answer :
In this case, the elevator acceleration is 1m/s2 and the maximum speed is 5m. You asked how far does the elevator move to accelerate until maximal speed. First, we need to calculate the time needed to accelerate until maximal speed. The calculation would be:
time = speed / acceleration= (5m/s) / (1m/s2)= 5s
Then to calculate the distance, the formula would be:
distance= (initial speed + final speed)/2 * time= (1+5)/2 * 5 = 15m
time = speed / acceleration= (5m/s) / (1m/s2)= 5s
Then to calculate the distance, the formula would be:
distance= (initial speed + final speed)/2 * time= (1+5)/2 * 5 = 15m
The distance covered by the elevator as it ascends from rest to its maximum speed is [tex]\boxed{12.5\text{ m}}[/tex].
Explanation:
Given:
The maximum speed of the hotel elevator is [tex]5\text{ m/s}[/tex].
The acceleration of the elevator is [tex]1\text{ m/s}^2[/tex].
Concept:
The elevator starts from rest and its speed increases as it moves up under the acceleration. The acceleration of the body is defined as the rate of change of velocity of the body.
The motion of the elevator under the acceleration is given by the third equation of motion.
[tex]\boxed{v^2_{f}={v^2_{i}}+2aS}[/tex]
Since the elevator starts from rest, the initial velocity of the elevator is zero and the final velocity of the elevator will be [tex]5\text{ m/s}[/tex].
Substitute the value of initial velocity, final velocity and acceleration in above expression.
[tex]\begin{aligned}(5)^2&=(0)^2+2(1)S\\S&=\dfrac{25}{2}\text{ m}\\&=12.5\text{ m}\end{aligned}[/tex]
Thus, The distance covered by the elevator as it ascends from rest to its maximum speed is [tex]\boxed{12.5\text{ m}}[/tex].
Learn More:
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3. Conservation of momentum of meteorite and car system https://brainly.com/question/6536722
Answer Details:
Grade: High School
Subject: Physics
Chapter: Laws of motion
Keywords:
elevator, ascends, acceleration, deceleration, initial velocity, final velocity, magnitude, maximum speed, distance.