Physics relative motion

Question

Statement : a man slides down the rope with a deceleration a relative to the rope.
Acceleration of man with respect it rope is taken as +a and not - a
Why is it so, why should we not take -a?

Answer 1

As David said, the question includes the tacit assumption that the upwards direction is positive.  Deceleration means that the absolute value of velocity is decreasing (the absolute value of velocity is also called speed).

 

If the man is sliding down the rope, he has a negative velocity (since downwards points in the negative direction).  If a is negative, then his velocity will decrease further still, leading to a HIGHER absolute value.  This would be an increase in speed.  So, a has to be positive, yielding an increase in velocity (velocity becomes more positive) but a decrease in speed (since v is now becoming closer, rather than further away from 0, through the negative numbers).

 

David does make one mistake; a match between the signs of velocity and acceleration yields an increase in speed, while a difference between them causes a decrease.  So for the man to speed up as he descends (an initially negative velocity becoming increasingly negative), his acceleration would also have to be negative.  The mistake is in assuming that a positive acceleration always increases speed; for this to happen, the signs of v and a have to be in agreement.

 

A minor, easily forgivable blemish on an Answers career of well-conceived, expertly written advice.

 

 

Answer 2

Position on rope is often "+" for higher and "-" for lower (but it could be reversed).

 

Velocity [that is, rate of change in position] usually has the same sign as position, since it is change in position divided by time (which is positive).

 

Acceleration is change in velocity over time.  The word "deceleration" means decreasing velocity, so "-" is used for deceleration.  That would be a situation where the man is slowing down as he descends.

 

If the man is speeding up as he descends, then acceleration would be "+" to indicate the increase in velocity.