IB DP Maths: AI HL复习笔记3.9.2 Constant & Variable Velocity
Vectors & Constant Velocity
How are vectors used to model linear motion?
- 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)
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|
Worked Example
Vectors & Variable Velocity
How are vectors used to model motion with variable velocity?
- 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
Exam Tip
- Look out for clues in the question as to whether you should treat the question as a constant or variable velocity problem
- 'moving at a constant speed' will imply using a linear model
- an object falling or rolling would imply variable velocity
Worked Example
a)Find the acceleration vector of the ball's motion.
b)Find the position vector of the ball at the time,?t.
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