A particle moves along a straight line and its velocity depends on time as v=6t−3t2 where v is in m/s and t in seconds. Find the average speed for first 4 seconds. (in m/s)
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Solution
For average speed =Total distanceTotal time Velocity, v=6t−3t2=3t(2−t) i.e., v≥0 for 0≤t≤2 and v≤0 for 2<t≤4 Thus, average speed =∣∣∫20vdt∣∣+∣∣∫42vdt∣∣∫40dt =∣∣6∫20tdt−3∫20t2dt∣∣+∣∣6∫42tdt−3∫42t2dt∣∣4 =|4|+|−20|4 =244=6m/sec