If an object is moving with constantvelocity 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
abe 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.