1. Basics

Speed = Distance / Time

Time = Distance / Speed

Distance = (Speed × Time)

2. Convert kilometres per hour(km/hr) to metres per second(m/s)

x km/hr = x * 5/18 m/sec

3. Convert metres per second(m/s) to kilometres per hour(km/hr)

x m/sec = x * 18/5 km/ hr

4. Average Speed

If an object covers a certain distance at xx kmph and an equal distance at yy kmph, the average speed of the whole journey

(2xy / x+y) kmph.

5. Relation Between Distance, Speed and Time

1. If the ratio of the speeds of A and B is a : b, then the ratio of the times taken by them to cover the same distance is

1/a : 1/b or b : a.

2. Speed and time are inversely proportional (when distance is constant)

Speed ∝ 1/time

3. Assume two objects A and B start at the same time in opposite directions from P and Q respectively. After passing each other, A reaches Q in aa seconds and B reaches P in bbseconds. Then,
Speed of A : Speed of B = root of b : root of a

4. An object covered a certain distance at a speed of vv kmph. If it had moved v1 kmph faster, it would have taken t1 hours less. If it had moved v2 kmph slower, it would have taken t2 hours more. Then,

v = v1v2(t1 + t2)/v1t2 - v2t1 kmph

x = vt1 (1 + v/v1) km

Special Case:
If t1=t2, v= 2v1v2/v1 - v2 kmph