Question
Sat July 14, 2012 By: Dhanraj Chaudhary

The speed-time graph of a particle moving along a fixed direction is shown in Fig. 3.28. Obtain the distance traversed by the particle between (a) t = 0 s to 10 s, (b) t = 2 s to 6 s.

Expert Reply
Sun July 15, 2012
 
Distance travelled will be the area under the speed time curve.
 
(a) Distance travelled is: 2 x 1/2 (5x12) = 60m
 
(b) Slope of upward increasing curve: 12/5 and of decreasing curve it is: -12/5
      This gives the rate of change of speed with time.
      Thus equation of line, speed at 2nd second will be:12/5*2 = 4.8 m/s
      Speed at 6th second: 12 - 12/5*1 = 48/5 = 9.6 m/s....  (because rate of change is negative
      and from 12 to 0)
      Thus total distance travelled = 1/2(12-4.8)(5-2) + 1/2(12-9.3)(6-5) = 12.15 m
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