Following are four different relations about displacement, velocity and acceleration for the motion of a particle in general. Choose the incorrect one (s)

Options

A. ` vec v _(av)= 1/2 [ vec v (t_1) + vec v (t_2)]`
B. ` vec v = ( vec r(t_2)- vecr (t_1))/(t_2-t_1)`
C. ` vec r = 1/2 ( vec v(t_2) - vec v (t_1)) (t_2-t_1)`
D. ` a_(av) = (vec v(t_2)- vec v(t_1))/(t_2-t_1)`

Answer

A, C

Explanation

For the motion of a particle if acceleration is not uniform then the relations
` vec v_(av) = 1/2 [ vec v(t-1) + vec v(t_2)] `si incorrect.
` vec v_(av) = (vec r(t_2) - vec r9t-1))/( (t_2-t_1)) ` is correct`.
` vec r = 1/2 [ vec v9t_2) - vec v( t-1) ] (t-2 -t_1) ` is incorrect, and ` vec a(av) = (vec v9t_1) - vec v(t_1))/(t_1 -t_1) ` is correct.