Constant & Variable Velocity (DP IB Applications & Interpretation (AI)) : Revision Note

If an object is moving with constant velocity it will travel in a straight line

For an object moving in a straight line in two or three dimensions its velocity, displacement and time can be related using the vector equation of a line

• r = a + λb

• Letting

  • r be the position of the object at the time, t

  • a be the position vector, r₀ at the start (t = 0)

  •  represent the time, t

  • b be the velocity vector, v

• Then the position of the object at the time, t can be given by

  • r = r₀ + tv

The velocity vector is the direction vector in the equation of the line

The speed of the object will be the magnitude of the velocity |v|

The velocity of a particle is the rate of change of its displacement over time

In one dimension velocity, v, is found be taking the derivative of the displacement, s, with respect to time, t

In more than one dimension vectors are used to represent motion

For displacement given as a function of time in the form

The velocity vector can be found by differentiating each component of the vector individually

• 

• 

• The velocity should be left as a vector

• The speed is the magnitude of the velocity

If the velocity vector is known, displacement can be found by integrating each component of the vector individually

• The constant of integration for each component will need to be found

The acceleration of a particle is the rate of change of its velocity over time

In one dimension acceleration, a, is found be taking the derivative of the velocity, v, with respect to time, t

In two dimensions acceleration can be found by differentiating each component of the velocity vector individually

If the acceleration vector is known, the velocity vector can be found by integrating each component of the acceleration vector individually

• The constant of integration for each component will need to be found