Question

A body travelling along a straight line traversed one third of the total distance with a velocity 4m/s . The remaining part of the distance was covered with a velocity 2m/s for half the time and with velocity 6m/s for the other half of time. Find the mean velocity averaged over the whole time of motion.​

Answer 1

Answer

Let total distance =d m

velocity in 1st 1/3rd distance =4m/s

time=d/12 s

remaining distance =2d/3

velocity in 1st half time(t) =2m/s

distance covered in 1st half time =2t

velocity in2nd half time =6m/s

distance covered in 2nd half time =6t

average velocity =2t+6t/t+t=4m/s

velocity in last 2/3rd distance =4m/s

time=d/6s

mean velocity = total distance /total time

$v = \frac{d}{ \frac{d}{12} + \frac{d}{6} } \\ v = \frac{1}{ \frac{1}{12} + \frac{1}{6} } \\ v = \frac{12}{3} \\ v = 4m {s}^{ - 2}$