Acceleration of a particle moving along a straight line If a particle moves along a straight line, then can we say that the acceleration should be zero? and if not, then why?
If the equation of the motion is linear, then the velocity is constant and if velocity is constant, then acceleration is zero.
 A: You are using the word "linear" in two different ways.
When an object moves along a straight line we can say its motion is linear - but that does not mean its acceleration is zero. Just that the acceleration points along the same direction as the velocity (so no change in the direction of the motion).
The second meaning of "linear" is in the exponents of the mathematical terms for the equation of motion - either time or position, for example.
The following equation describes linear motion with acceleration:
$$\vec r(t)= (a\cdot t^2, 0)$$
This is uniform acceleration along the X axis. It is "linear" in the sense of moving along a line.
Now if position is a linear function of time (which is a much narrower reading of "linear motion"), then and only then can you say the velocity is constant and the acceleration is zero.
A: Velocity is a vector quantity having both magnitude and direction. Change in either one of these or both is acceleration. A body moving along a straight path would have constant direction but might have variable speed.
A: Consider a mass which is dropped from a height. This is done in a vacuum, or is otherwise shielded from crosswinds. Furthermore, the mass is located on a non-rotating body, has no lateral initial velocity, and is not noticeably affected by the gravitation of any other bodies.
Two things are clear: first, the mass moves in a straight line toward the center of the body; second, it accelerates along that straight line.
The phrase "a particle moves along a straight line" may or may not be used to describe motion described by a linear equation, and in the more general sense does not imply this meaning. To describe a path as being governed by a linear equation usually means something like (for 2D paths) y = ax + b. Note that this description of the path says nothing about the velocity of a point along the path - it might be constant, or it might not. 
A: If your direction of motion is linear it does not necessary mean that the equation representing its position with respect to time is always linear.And if the velocity is constant it always means that acceleration is zero.
