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.
转载自savemyexam
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