A vehicle travels different distances with different speeds in the same direction. Find the expression for the average speed of a vehicle.

Explanation

Suppose, a vehicle travels different distances `d _(1), d _(2), d _(3),…` with different speeds `v _(1), v _(2) , v _(3),…` respectively in the same direction.
Total distance travelled, `D = d _(1) + d_(2) +d _(3) +..`
Total time taken, `t = t _(1) +t _(2) + t _(3) +...`
But time `= ("distance")/("velcity")`
`therefore t _(1) +t _(2) +t_(3) +...=(d _(1))/(v_(1)) + (d_(2))/(v_(2)) + (d_(3))/(v_(3)) +...`
Average speed `= (D)/(t) = (d_(1) +d _(2) + d _(3) +...)/( (d_(1))/( v _(1) ) + (d_(2))/(v _(2)) + (d_(3))/( v _(3)) + ...)`