# Displacement -calc

1. Sep 1, 2006

### konichiwa2x

The displacement 'x' of a particle varies with time according to the relation
$$x = \frac{a}{b}(1 - e^-^b^t)$$ Then,

(A) At t=1/b the displacement of the particle is a/b.
(B) The velocity and acceleration of the particle at t=0 are 'a' and 'b' respectively.
(C) The particle cannot reach a point at a distance 'x' from its starting point if x'>ab.
(D) The particle will come back to its starting point as 't' tends to infinity.

I have differentiated to obtain the velocity and also acceleration but I still cant seem to solve this.

2. Sep 1, 2006

### Päällikkö

Have you noticed why a, b and d are not correct?
The particle is at its maximum distance when its velocity is zero.

3. Sep 1, 2006

### Saketh

This is just plugging in and checking.
You said you differentiated to get the velocity and acceleration functions, so this is just more plugging in and checking. If you are unsure, you probably differentiated incorrectly.
In order for it to come back, its velocity would need to change direction at some point. Does it? And if so, does it reach the starting point again?