What's the problem with my shift solenoid? Is this the cause of the rumbling?

What is your question?

The rumbling starts after I start to drive my car. After driving for a longer period of time, the RPM increases but the speed doesn't increase with it. Every time I stop at a red light or stop sign, I have to worry about the rumbling starting once I drive again.

What makes this problem better or worse?

The longer I drive the car

How long has your 2013 Nissan Pathfinder had this problem?

A couple of days