Question

An elevator is moving downward when someone presses the emergency stop button. The elevator comes to rest a short time later. Give the signs for the velocity and the acceleration of the elevator after the button has been pressed but before the elevator has stopped.Enter the correct sign for the elevator's velocity and the correct sign for the elevator's acceleration, separated by a comma. For example, if you think that the velocity is positive and the acceleration is negative, then you would enter +,- . If you think that both are zero, then you would enter 0,0 .

Answer 1

Answer: - , +

Step-by-step explanation:

Velocity and Acceleration

In general terms, velocity and acceleration in the plane are both vectors with two components. They don't have 'sign' but magnitude and direction. If we know motion is restricted to a simple line, then we can define the positive and negative references.

In vertical motion, the positive reference is commonly pointed upwards, but if we chose the opposite way, the results shouldn't change in magnitude, just their signs. Let's choose like proposed, the positive direction upwards.

Since the elevator was moving downwards, its velocity is negative. When the button is pushed, it continues to move downwards, but slower. Its velocity is still negative.

The acceleration has the same sign as the velocity if it tends to increase the magnitude of the object, and is negative in the opposite case. Let's look at the formula

`\displaystyle a=(v_f-v_o)/(t)`

In this case,
`v_f=0` because the elevator will eventually stop, and
`v_o` is negative. It means the acceleration is

`\displaystyle a=(-v_o)/(t)`

It results in a positive value

`\boxed{Answer: -,+}`

Note: If we chose the opposite references, then the answer would be: +,-