Velocity versus displacement graph of a particle moving in a straight line as shown in figure. The acceleration of the particle

From the graph, velocity-displacement equation can be written as v=v0+αx …….(i)Here v0 and α are positive constants. Differentiating Eq. (i) with respect to x, we get dvdx=α= constant Acceleration of the particle can be written as a=vdvdx=v0+αxαThe a-x equation is a linear equation. Thus acceleration increases linearly with x.