   # Motion of Point-Mass Objects in Two and Three Dimensions  Q:     At what point in the path of a projectile is the speed a minimum? A:    The speed of the projectile is at a minimum when the projectile has reached its highest point.  This is because the projectile only has horizontal speed, the vertical speed has gone to zero and is about to reverse direction. Q:     At what point in the path of a projectile is the speed a maximum? A:    The projectile has its maximum speed at the lowest point along its path.  Here the projectile not only has its horizontal velocity but also has a maximum vertical velocity, downwards.

## References

### Equations

 Position vector r = xi + yj + zk Displacement r = r2 - r1 r = (x2 - x1)i + (y2 -y1)j + (z2 -z1)k Average velocity Velocity v = vx i + vy j + vz k Average acceleration Acceleration a = ax i + ay j + az k Projectile motion x - x0 = (v0 cos 0 ) t y - y0 = (v0 sin 0) t - gt2 vy = v0 sin 0 - gt Path of a particle in projectile motion Range of a particle in projectile motion Uniform circular motion Time for a particle in in uniform circular motion to complete a circle Relative motion vPA = vPB +  vBA aPA = aPB # Mechanics List of Topics

 Measurements Newton's Laws Potential Energy and Conservation of Energy Rotation of Rigid Bodies Elasticity Vectors Forces and Fields Linear Momentum Angular Momentum Mechanical Oscillations Motion of Point-Mass Objects in One Dimension The Gravitational Field Collisions Torque Mechanical Waves Motion of Point-Mass Objects in Two and Three Dimensions Kinetic Energy and Work Circular Motion of Point-Mass Objects Equilibrium Sound  ครั้งที่

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