You want to visit your friend in Seattle during spring break. Tosave money, you

Question

You want to visit your friend in Seattle during spring break. Tosave money, you decide to travel there by train. Unfortunately,your physics final exam took the full 3 hours, so you are late inarriving at the train station. You run as fast as you can, but justas you reach the platform you see your train, 30 m ahead of youdown the platform, begin to accelerate at 1.0 m/s^2. Youchase after the train at your maximum speed of 8.0 m/s, but there'sa barrier 50 m ahead. Will you be able to leap onto the backstep of the train before you crash into the barrier?

Explanation / Answer

time is distance divided by velocity. So you will reachthe wall in: 50 m / 8 m/s = 6.25 s So the question is will you arrive at the back of the trainsooner than this? The train begins from rest and accelerates at 1 m/s^2. Velocity is acceleration * time. Average velocity is half ofthis since it started from rest. Distance is velocity *time. And it has a 30 meter head start. So its distancecan be expressed as dtrain= 30 m+0.5 * (1 m/s^2) * t^2 And your distance is dyou=(8 m/s) t At some point, you will reach the back of the train. i.e. your distances will be equal. So set the above equationsequal to each other and solve for time (30 m) + 0.5 (1 m/s^2) * t^2 = (8 m/s) t (0.5 m/s^2) t2 - (8 m/s) t + (30 m) = 0 Use the quadratic equation. You get 6 and 10. So at 6 seconds, you catch up to the train, and if you keptrunning and the wall wasn't in the way, you'd pass the back of thetrain, and at 10 seconds, it would catch back up to you. Soyou have 2 opportunities to jump on the train, at 6 seconds and at10 seconds, but 10 seconds won't work since the barrier will stopyou at 6.25 s.

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