A particle is moving along $x$-axis whose position is varying with time according to x=-3t+$t^3$. The displacement from t=1 to t=3 is

Question

This question is as simple as the just substituting the values (that’s what I think, doesn’t have to be right). So we get

For $t=1$ $$x=-3+1=-2$$

For $t=3$ $$x=-9+27=18$$

Adding both we get $+16$ . The answer given is $20$ . Why is this so?

Answer 1

It's simple, you have to add the absolute values .The negative sign in coordinate of $x$ indicates that its 2 units away from origin in opposite direction. you should draw a diagram to see it clearly.

Answer 2

Body start from -2 and go to + 18 then total displacement will be +20

Answer 3

The initial position of the particle is $-2$ and the final position is $1$. So displacement is $final \;position - initial\; position$ $=18-(-2)$ $=18+2$ $=20$

Answer 4

As others have noted, the answer is $20$ because the computation involves $18 - (-2) = 20$. More generally, displacement is defined as an object's final position minus its initial position. Note that this doesn't have anything to do with absolute values, actually—you can have a negative displacement!