Mars Curiosity speed and entry

My understanding is that Earth’s escape velocity is in the neighborhood of 25,000 mph and that speed decreases with distance. NASA’s curiosity web site lists curiosity’s current speed at around 115,000 kph, roughly 68,000 mph. I was surprised that it was going this fast! I had anticipated somewhere around escape velocity (I realize that escape velocity doesn’t impact how fast it could travel to Mars. Only that a significant portion of fuel would be used just to get up and out of here and didn’t seem like there’d be much left to get it to that velocity) .

If I read this correctly, Curiosity will enter the Martian atmosphere at around 13,000 mph.

The spacecraft only has small thrusters for course correction as I understand it, so how does it get from a 68,000 mph cruise to 13,000 mph just before entry?

68,000 mph relative to what? Your final question is only valid if this is the speed relative to Mars.

Where exactly is that number given?

I suspect the 115,000 kph speed is the orbital speed relative to the sun, while the 13,000 mph reentry speed is relative to Mars. Escape velocity is given relative to the body you’re escaping from.

Yup.