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A car starts moving rectilinearly, first with acceleration [tex] \omega = 5.0 [/tex] m/s^2 (the initial velocity is equal to zero), then uniformly, and finally, decelerating at the same rate [tex] \omega [/tex], comes to a stop. The total time of motion equals [tex] \tau = 25 [/tex] s. The average velocity during that time is equal to [tex] v = 72 [/tex] km per hour. How long does the car move uniformly?

If I did not have to deal with the average velocity, then I can figure out that the car will reach a maximum speed of 50 m/s for an instant before it has to decelerate in order to have a 25 s trip. But I think this is where I have a weakness when it comes to average velocities. How do you put it together with acceleration? The answer at the back of my book gives a result of 15 s. I'd appreciate any help getting me pointed in the right direction.