The following are four different relations about displacement, velocity and acceleration for the motion of a particle in general.

(a) \(v_{a v}=1 / 2\left[v\left(t_1\right)+v\left(t_2\right)\right]\)
(b) \(v_{{av}}={r}\left({t}_2\right)-{r}\left({t}_1\right) / {t}_2-{t}_1\)
(c) \(r=1 / 2\left[v\left(t_2\right)-v\left(t_1\right)\right]\left({t}_2-{t}_1\right)\)
(d) \({a}_{{av}}=v\left({t}_2\right)-v\left({t}_1\right) / {t}_2-{t}_1\)


The incorrect alternative/s is/are:

1. (a), (d) 2. (a), (c)
3. (b), (c) 4. (a), (b)

(2) Hint: Recall the concept of average velocity and average acceleration.

Step 1: Find the average velocity of the object.

If an object undergoes a displacement Ar in time At, its average velocity is given by
v=ΔrΔt=r2r1t2t1 where r1 and r2 are position vectors corresponding to time t, and t

Step 2: Find the average acceleration.
t the velocity of an object changes from v, to v in time At. Average acceleration is given by
aav=ΔvΔt=v2v1t2t2
But, when acceleration is non-uniform,

                         vav  v1 + v22We can write    Δv = ΔrΔtHence,               Δr = r2  r1=(v2  v1)(t2  t1)