A student is running at her top speed of 5.0 m/s to catch a bus…

Question

A student is running at her top speed of 5.0 m/s to catch a bus, which is stopped at the bus stop. When the student is still 40.0 m from the bus, it…

Jason · Accepted Answer

(a) The student must run for approximately $ 9.55 \, \text{s} $ and cover $ 47.77 \, \text{m} $.
(b) When she reaches the bus, it is traveling at $ 1.62 \, \text{m/s} $.
(c) **Graph Description**:
&#8211; Student&#8217;s Path: A straight line with constant slope at $ 5.0 \, \text{m/s} $.
&#8211; Bus&#8217;s Path: A parabola starting at $ 40.0 \, \text{m} $ with increasing slope.
(d) Second solution $ t \approx 49.27 \, \text{s} $ represents when the bus overtakes the student again. Bus speed at that time: $ 8.38 \, \text{m/s} $.
(e) If the student&#8217;s top speed is $ 3.5 \, \text{m/s} $, she will not catch the bus (no real solution, $ D < 0 $).
(f) Minimum speed to catch the bus: $ 3.69 \, \text{m/s} $, time $ 21.72 \, \text{s} $, covering $ 80.17 \, \text{m} $.

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