Short Cut Formulas -Time, Speed and Distance

Time, Speed and Distance

BASIC Formulas for Time and speed calculations:

1. (a) Total Distance 'd' covered by a body traveling at a speed 's' with 't' as the  

         time of travel is given by

                            d = s x t

   (b). Total  time taken by a body to cover a distance 'd' in when traveling at a 

         speed 's' is given by 

                           t = d/s

   (c)  Speed of a body that covered a distance of 'd' in time 't' is

                           s = d/s

TIPS And TRICKS:

1. To convert speed in km/hr to m/s, multiply the given speed by (5/18)  to get the speed in m/s.

for example to convert the speed 40km/hr to speed in m/s, multiply 40 by (5/18) to get  40 km/hr = (40)x(5/18) m/s = 11.11 m/s

2. To convert speed in m/s to km/hr, multiply the given speed by (18/5)  to get the speed in km/hr.

for example to convert the speed  20 m/s to speed in km/hr multiply 20 by (18/5) to get 20m/s = (20)x(18/5) km/hr =  72 km/hr

3. For the types of questions where we have to find the average speed when two equal distances are traveled with different speeds, say x and y , the formula is

                    average speed = (2xy) /(x + y) 

    (a)  when there are 3 speeds(x,y,z) involved then, the formula is 

                   average speed = (3xyz)/ (xy + yz +zx )  

 

    (b) when there are 4 speeds (w,x,y,z) involved then, the formula is 

                   average speed = (4xyz)/ (xyz + yz +zx )  

4. For the type of questions where a distance is traveled at different speeds (x and y )from the usual speed and the difference of time from the usual time taken is given, we use the formula to get the distance as 

      Distance = [(x x y)( x- y)]x(t1 - t2)

  

      Note: (i) for time t1 and t2, use different signs (+ve, -ve) for someone 

                   being late or early. 

               (ii) if someone is late while traveling at the given speeds use the 

                   same sign for both the situations. The same is applied when some 

                   one is  early in both the situation.

5. If two bodies are traveling opposite to each other at x km/hr and y km/hr respectively,then the relative speed would be (x + y) km/hr

6. If two bodies are traveling opposite to each other at x km/hr and y km/hr respectively,then the relative speed would be (x - y) km/hr                 

7. Distance covered by a train while crossing a point ( a person or post) is the length of the train itself.

8. Distance covered by a train while crossing a platform ( of length L) is equal to the sum of the length of the platform and the length of the train.

9. Distance covered by a train of length L while crossing another train of length M
    is equal to (L + M).
  
10. If someone travels the same distance with different speeds(s1 and s2) and 
      hence arrive at different times (t1 and t2), then the formula for getting the 
      distance is 

         Distance = {(s1 x s2)/(s1 - s2)}x (t1 - t2)
  

Note: The units of speed, distance and time should be consistent. 

1. If the distance is given in kilometer and speed is given in km/hr, then the unit    of the time should be in hours.  

2. If the distance and speed are in meter and meter/seconds then unit of time should be in seconds.wrong units can result in wrong answer.

Want to have a look at the applications of the above formula 

read: Solved questions on Time Speed and Distance