The given graph shows the variation of velocity (v) with position (x) for a particle moving along a straight line Which of the following graph shows the variation of acceleration (a) with position (x)?

Step-by-step solution

(A) Given line have positive intercept but negative slope. So its equation can be written as, ( v=-m x+v₀ (1) ) where ( m= = v₀ x₀ ) By differentiating with respect to time we get, ( d v d t =-m d x d t =-m v ) Now substituting the value of ' ( v ) ' from equation (1) we get ( d v d x =-m [-m x+v₀ ]=m² x-m v₀ ) ( a=m² x-m v₀ ) i.e., the graph between a and ( x ) should have positive slope but negative intercept on acceleration axis. Hence option (A) is correct.