Question

Which of the following combinations of position (x) and direction of motion would give a velocity in the x-direction that has a negative value?

a. Positive x, moving towards the origin.

b. Negative x, moving away from the origin.

c. Both a and b.

d. Positive x, moving away from the origin.

e. Negative x, moving towards the origin.

Answer 1

Velocity is given by:

V = dX/dt

V = (Xf - Xi)/dt

Xf = final position

Xi = initial position

Now check option A.

when positive x, moving towards origin, then

Xf < Xi (Since moving towards origin)

Xf - Xi < 0

So, Xf - Xi = negative, which means

dt = will always be positive, as tf > ti

V = (Xf - Xi)/dt = negative quantity/positive quantity = negative

So velocity will be negative

Now Option B.

Negative x, moving away from the origin

Since x is negative, So

Xf < Xi

Xf - Xi < 0

Xf - Xi = negative

(take an example to understand that if Xi = -2 m and Xf = -5 m, since given that moving away from origin, then Xf - Xi = -5 - (-2) = -3)

So in this case too

V = (Xf - Xi)/dt = negative/positive = negative quantity

So velocity will be negative.

Correct option will be C.

Please Upvote.

In option D and E velocity will be positive.