Question

the elevators in the landmark tower, in yokohama, japan, are among the fastest in the world. they accelerate upward at 3.125 m/s² for 4.0 s to reach their final speed. if these elevators start from rest, what is their final speed?

Explanation:

Step1: Recall the kinematic equation for velocity

The kinematic equation for final velocity \( v \) when an object starts from rest (\( u = 0 \)) and undergoes constant acceleration \( a \) for time \( t \) is \( v=u + at \). Since the elevator starts from rest, \( u = 0\space m/s \).

Step2: Substitute the given values

We are given \( a = 3.125\space m/s^{2} \) and \( t = 4.0\space s \), and \( u = 0\space m/s \). Substituting these into the equation \( v=u+at \), we get \( v = 0+(3.125\times4.0) \).

Step3: Calculate the final velocity

Calculating \( 3.125\times4.0 \), we have \( 3.125\times4.0 = 12.5\space m/s \).

Answer:

The final speed of the elevator is \( 12.5\space m/s \).