. Explain the difference between average rate of change and instantaneous rate of change. Provide specific examples

Answer 1

when the posted speed limit says 70 mph, it refers to instantaneous rate of change.

It's not a defense to say your average speed was only 65 mph

You could prove you drove for 1 hours and traveled 65 miles, which means just 65 mph average speed, but if at any point during that hour you drive faster than 70 mph, you may get a speeding ticket

the police officers' radar measures instantaneous rate of speed, not average speed. It measures instantaneous rate of change of distance = instantaneous speed or velocity.

You go 75 mph for half an hour, then 65 mph for half an hour

you travel 75/2 + 65/2 = 140/2 = 70 miles in one hour. You average speed is 70 mph

Your instantaneous speed was 75 mph for 1/2 an hour, and 65 mph for 1/2 an hour

for half an hour you might see some flashing red lights in your rear view mirror