# Motion on a curvy track

BACKGROUND

The path kinematics description has taught us the following things:

• Velocity is always TANGENT to the path.
• Acceleration, in general, has BOTH tangential and normal components.
• The normal component of acceleration always points INWARD to the path.
• The tangential component direction depends on how the point P is changing in speed. If the speed is INCREASING, angle θ between the velocity and acceleration vectors is in the range of:  0 ≤ θ< 90°; that is, the tangential component points forward of the motion.
• If the speed is DECREASING, angle θ between the velocity and acceleration vectors is in the range of:  90° < θ ≤ 180°; that is, the tangential component points rearward of the motion.

Shown below is an animation made from a simulation of an object moving along on a curvy path. The speed of the object goes through cycles of increasing and decreasing speed. The velocity and acceleration vectors for the object are shown in blue and red, respectively. Can you make the above observations on the motion shown below of this object?