Question

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

1. `v_(av) = 1/2 [v(t_1) + v(t_2)]`
2. `v_(av) = (r(t_2) - r(t_1))/(t_2 - t_1)`
3. `r = 1/2 (v(t_2) - v(t_1))(t_2 - t_1)`
4. `a_(av) = (v(t_2) - v(t_1))/(t_2 - t_1)`

Answer 1

a and c

Explanation:

If an object  undergoes s displacement Δr in time Δ t, its average velocity is given by v = `(Δr)/(Δt) = (r_2 - r_1)/(t_2 - t_1)`; where t₁ and r₂ are position vectors corresponding to time t₁ and t₂.

 It the velocity of an object changes from v₁ to v₂ in time Δt. 

 Average acceleration is given by `a_(av) = (Δv)/(Δt) = (v_2 - v_1)/(t_2 - t_1)`

But, when acceleration is non-uniform

`v_(av) ≠ (v_1 + v_2)/2`

We can write `Δv = (Δr)/(Δt)`

Hence, `Δr = r_2 - r_1 = (v_2 - v_1) (t_2 - t_1)`.