An elevator is descending at a velocity of -2 m/s with an acceleration of +3.0 m/s^2 .

Question

In this "elevator problem" with known velocity and acceleration, you must construct a free-body diagram of the elevator or the person inside and state whether the velocity is increasing or decreasing.

Answer 1

If the elevator is traveling with an initial velocity of -2 m/s, that means that the elevator is traveling downward. This is because the sign of the vector, in this case negative, give you the direction. Down is negative in our standard coordinate plane.

If the acceleration is +3.0 m/s², the acceleration of the elevator is pointing upward for the same logic that we used before.

When you have an acceleration and velocity parallel (pointing in the same direction) to one another, that object is speeding up, regardless of the sign! When you have an acceleration and velocity that are antiparallel (pointing in opposite directions), the object is slowing down. For this elevator, velocity and acceleration are antiparallel, therefore the elevator is slowing down.

Assuming the elevator is a simple one, there will be only two external forces on the object, and therefore two force vectors on our free body diagram (FBD). The tension in the cable pointing upward, and gravitational force pointing downward. If we are only sketching the FBD, we only need the proportionality (i.e. the relative lengths) of the vectors to be accurate.

Since there is a net acceleration upward (remember +3.0 m/s²), then there MUST be a net external force upward. Newton's 2nd law can be written in the form F_net = ma_net. If there is a net force upward, then the upward tension force MUST be larger than the downward gravitational force. This is shown on our FBD as a longer tension force vector, relative to gravitational force.