Kinematics (1D)

1. Direction of motion

1.1. Direction of motion is given by velocity

2. Equation of motion

2.1. v=u+at S=ut+1/2at^2 v^2=u^2+2aS

2.2. The 's' here is displacement and not distance

3. Graphs

3.1. S-t graph

3.1.1. Slope=velocity

3.2. V-t graph

3.2.1. Slope= acceleration Area = distance + displacement

3.3. a-t graph

3.3.1. Slope= jerk Area= change in velocity

3.4. Hacks

3.4.1. Upward concave(bowl) a=+ve Downward concave (up side down bowl) a=-ve

3.4.2. Velocity acceleration same sign; speed increase Velocity acceleration different sign ; speed negative

3.4.3. Angle formed by tangent on x axis < 90° = velocity is +ve Angle formed by tangent on x axis > 90° = velocity is -ve

4. Relative velocity

4.1. ⊙Vab=Va-Vb (velocity of a with resp to b) ⊙Time + relative distance does not depend on frame of reference. ⊙under gravity relative acc = 0

5. Distance and displacement

5.1. Distance: scalar (S=$vdt) Displacement: vector Distance >= Displacement

6. Speed and velocity

6.1. Speed= Distance/ Time Scalar quantity

6.2. Velocity = Displacement/Time Vector quantity

6.3. Average speed = total distance/ total time

6.4. Average velocity = total displacement/ total time

7. Instantaneous velocity

7.1. (When time is very small) V(inst) =dS/dt

8. Displacement in nth second

8.1. S (nth)= S(n)-S(n-1)

9. Acceleration

9.1. a=dV/dt v=$adt a=v dv/dt

10. Motion under gravity

10.1. a=g=9.8/10m/s^2 a is constant

10.1.1. When point body is/thrown above reference point: Speed, displacement will be positive Acceleration negative

10.1.2. When point body is/thrown below reference point: Speed, displacement will be negative Acceleration negative

10.1.3. Tower sums will have initial and final position = height of tower