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Q.
A car covers the first half of the distance between two places at 40 km/h and another half at 60 km/h. The average speed of the car is
AIPMTAIPMT 1990Motion in a Straight Line
Solution:
Letx consider, $x =$ total distance covered by the car, Time taken to complete the half distance with velocity $v =40\, km / h$,
$t _{1}=\frac{ x }{2 \times 40}=\frac{ x }{80} hr \ldots . .(1)$
The time taken to complete another half distance with velocity $u =60 km / h$
$t _{2}=\frac{ x }{2 \times 60}=\frac{ x }{120} h$
The total time taken, $t = t _{1}+ t _{2}$
$t =\frac{ x }{80}+\frac{ x }{120}=\frac{ x }{48} h$
The average speed of the car,
$v _{ avg }=\frac{ x }{ x / 48}=48 km / h$