How long does it take an automobile traveling in the lane of a highway at 65.0 km/h to overtake (become even with ) another car that is traveling in the right lane at 25.0 km/h when the car from bumpers are initially 80 m apart ?

1 Answer
Steve J.
Jun 6, 2018

#"time" = 7.2 s#

Explanation:

The slower car sees the faster car approaching at a relative speed of #65 (km)/h - 25 (km)/h = 40 (km)/h#.
The initial distance between them was 80 m, which is equivalent to 0.08 km.

How to use that data to get a result:

  • #"speed" = "distance"/"time"#, therefore after an application of some algebra,

#" ""time" = "distance"/"speed"#

  • Plugging in the data, we find that

#" ""time" = (0.08 cancel(km))/(40 cancel(km)/h) = 0.002 h#

Perhaps it would be better to know how many seconds that is ...

#0.002 cancel(h) * (3600 s)/(1 cancel(h)) = 7.2 s#

I hope this helps,
Steve

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