1. Speed, Time and Distance:
Speed = (Distance / TIme)
Time = (Distance / Speed)
Distance = (Speed * Time)
2. km/hr to m/sec conversion:
x km/hr = (x * 5/18) m/sec
3. m/sec to km/hr conversion:
x m/sec = (x * 18/5)km/hr
4. If the ratio of the speeds of A and B is a : b, then the ratio of the the times taken by then to cover the same distance is 1/a: 1/b or b: a
5. Suppose a man covers a certain distance at x km/hr and an equal distance at ykm/hr. Then,the average speed during the whole journey is [2xy/(x+y)]km/hr
Average speed= Total distance traveled/Total time taken
When the body travels at ‘u’ m/s for t1 seconds and ‘v’ m/s for t2 seconds, then
Average speed= (ut1+vt2)/(t1+t2).
There are other aspects of finding average speed
When the body travels ‘L’ distance at ‘u’ m/s and ‘M’ distance at ‘v’ m/s; Average speed = (Mu+Lv)/(L+M)
Stream: Moving water of the river is called stream.
Relative Speed: Speed of a moving body with respect to another moving body is called relative speed.
Speed of A with respect to B is as follows:-
When they are moving in same direction; Relative speed of A= A-B
When they are moving in opposite direction; Relative speed of A= A+B
Key points on Trains:
When a train is crossing a pole distance traveled by the train= length of train
When a train of length L is crossing a bridge of length B; the distance traveled by train=L+B
When a train of length L is crossing a platform of length P; then distance traveled by train=L+P
When a train of length L1 is crossing/ overtaking another train L2; then distance traveled = L1+ L2
Key points on Downstream/Upstream:
Definition: In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream.
Still Water: If the water is not moving then it is called still water.
If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:
Speed downstream = (u + v) km/hr.
Speed upstream = (u – v) km/hr.
If the speed downstream is a km/hr and the speed upstream is b km/hr, then:
Speed in still water =(a+b)/2km/hr
Rate of stream=(a-b)/2 km/hr
Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?
Let the distance travelled by x km.
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr =(60/10)hours = 6 hours
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed =(60/5)kmph = 12 kmph