Study each gauge separately.  Concentrate on the velocity gauge.  Note that it stays the same length, the constant speed of the car.  It does, however, change; it changes in direction.  It always points in the direction the car is moving.

Concentrate on the acceleration gauge.  When the velocity isn't changing (neither magnitude nor direction), the acceleration is zero, as represented by the blue dot at the center of the gauge.  But when the car starts its turn, its velocity changes (the speed doesn't).  The acceleration gauge shows the velocity of the tip of the velocity gauge; it shows the car accelerating toward the center of the circle of the car's motion.  (The center of the circle, and a line from the center to the car, are shown while the car is turning.  This helps us see that the direction of the acceleration is, for this "uniform circular motion,"  toward the center of  the circle.)

Next, ask yourself what force on the car would be needed to change its motion as it rounds the curve.  Newton's second law of motion is the clue.  It says force and rate of change of motion (acceleration) go hand in hand.  Graphically they are equivalent.  That means that the blue arrow can represent that force.  Imagine you are playing a computer game where you direct the motion of the car with pressure on a joy stick.  That blue arrow is your guide telling you what force you need to put on the joy stick.  If the blue arrow is too long, the car will veer off the right side of the road; if too short, the car won't turn sharply enough and will run off the left side of the road.  (When the blue arrow is just a dot, the car travels in a straight line at constant speed.)

What are the forces on the car while it's turning?

There is a force of gravity on the car pulling downward.  There is also a force of the road pushing upward to exactly balance that force of gravity: those two forces exactly cancel.  But when the car is turning, an additional force has to do the accelerating: something has to take the place of the game player with the joy stick.  (Don't abandon physics now: "acceleration" does not  mean "going faster." It means time rate of change of velocity.)  It's the road appling a frictional force to the tires.  (The acceleration is proportional to the force: what is the constant of proportionality?)  Icy roads teach a lot about Newton's laws.  Icy roads don't have much friction. Icy roads don't always apply enough force on the tires to cause the needed acceleration toward the center of the cricle.  Then the car tries to go as Newton's first law of motion states: in a straight line...and off the road!

Now, imagine you are in the a passenger, please.  In the back seat, behind the driver.  Shut your eyes.  When you go into the turn, you will feel additional forces on your body.  Just what and where is pushing on you that wasn't while you were travelling straight?  If your eyes were open, you probably would sense that something is pushing on you toward the outside of the curve; toward your left.  But that's your egocentrism taking control.  The little frame of reference you carry about with you sees your body being flung toward the outside of the curve: a "centrifugal fling"!  But your eyes are shut.  What you are actually feeling is a new force pushing on you by the wall of the inside of the car, the wall on your left.  It's pushing you toward the right.  That's the way your body is accelerating: toward the center of the curve.

Now rethink the motion of the bouncing ball.  Imagine its velocity gauge.  Imagine its acceleration gauge.  [Check in here, then come back to this page.]