Question

A car travels along a straight line at a constant speed of 53.0 mi/h for a distance d and then another distance d in the same direction at another constant speed. the average velocity for the entire trip is 26.5 mi/h. (a) what is the constant speed with which the car moved during the second distance d?

Answer 1

A distance of d is covered with 53 mile/hr initially. Time taken to cover this distance t1 = d/53 hour Next distance of d is covered with x mile hours. Time taken to cover this distance t2 = d/x hours. We have average speed = 26.5 mile / hour

= Total distance traveled/ total time taken

=
`(2d)/((d)/(53)+(d)/(x)) = (2)/((1)/(53)+(1)/(x) )  = (106x)/(x+53)`

`26.5 = (106x)/(x+53) \\ \\ 79.5 x = 1404.5\\ \\ x = 17.67 miles/hour`