Question

The velocity of a particle moving along x axis varies with its position x as v=alpha root x; where alpha is a constant. What will be the graph that represents the variation of its acceleration (a) with time(t)

Answer 1

The acceleration of the particle is given by:
[tex]a=v \frac{dv}{ds} [/tex]
$v= \alpha \sqrt{x} \\ \frac{dv}{dx} = \frac{ \alpha }{2 \sqrt{x}} \\ a= \alpha \sqrt{x} \times \frac{ \alpha }{2 \sqrt{x} } = \frac{ \alpha ^2}{2}$
Hence acceleration of particle is contant and doesn't vary with time. The graph will be a horizontal line with acceleration having value equal to $\alpha ^2/2$