A particle moves such that its position vector where is a constant and is time. Then which of the following statements is true for the velocity and acceleration of the particle :
is perpendicular to and is directed towards the origin
Step 1: Given data.
A particle moving with a position vector
Step 2: Finding the velocity vector and acceleration vector of the particle.
We have,
We know that,
Where is the velocity vector.
….
Again,
Where is the acceleration vector.
…
Where the negative sign shows that acceleration is antiparallel to the position of the particle.
Therefore.
So, from above it is clear that is perpendicular to .
Hence, option A is correct.