IIT JEE Physics Formula Revision 3. Rest and motion :kinematics

1. v_av = s/(t2 - t1)
where v_av = average speed

2. v = limΔt→0 Δs/Δt = ds/dt
where v = instantaneous speed

3. s = ∫vdt from t1 to t2
where s = distance travelled during time t1 to t2

4. v_av = (r2 - r1)/(t2-t1)
Where
v_av = average velocity
r2, r1 = position vectors of a particle
t2, t1 = time instants

5. v = lim Δt→0 Δr/Δt = dr/dt

6. v = |dr|/dt = ds/dt
Where v = magnitude of velocity
s = displacement, for small time intervals magnitude of displacement will be equal to distance.

7. a_av = (v2 - v1)/(t2-t1)

8. a = lim Δt→0 Δv/Δt = dv/dt

For Motion in straight line

9. Velocity is v = dx/dt
10. a = dv/dt
11. acceleration is a = dv/dt = d²x/dt²

For constant acceleration
12. v = u+at
13. x = distance moved in time t = ut+½at²
14. v² = u²+2ax

For motion in plane

22. Time of flight of the projectile = (2u sin θ)/g

23. OB = (u²sin 2θ)/g

24. t = (u sin θ)/g
At t vertical component of velocity is zero.

25. Maximum height reached by the projectile (in t = (u sin θ)/g) = (u² sin²θ)/2g

27. V(B,S) = V(B,S')+V(S',S)

Where
V(B,S) = velocity of body wrt to S)
V(B,S') = velocity of body wrt to S')
V(S',S) = velocity of S' wrt to S)

we can rewrite above equation as

28. V(B,S') = V(B,S)- V(S',S)