A student is running at her top speed of 4.6 m/s to catch a bus, which is stoppe
ID: 1445810 • Letter: A
Question
A student is running at her top speed of 4.6 m/s to catch a bus, which is stopped at the bus stop. When the student is still a distance 41.2 m from the bus, it starts to pull away, moving with a constant acceleration of 0.163 m/s2 .
1) For how much time does the student have to run at 4.6 m/s before she overtakes the bus?
2) For what distance does the student have to run at 4.6 m/s before she overtakes the bus?
3) When she reaches the bus, how fast is the bus traveling?
4) If the student's top speed is 3.00 m/s , will she catch the bus?
5) What is the minimum speed the student must have to just catch up with the bus?
6) For what time does she have to run in that case?
7) For what distance does she have to run in that case?
Explanation / Answer
given:v=4.6m/s, s=41.2,a=0.163m/s^2
1) For how much time does the student have to run at 4.6 m/s before she overtakes the bus?
catches bus
Distance the student must run = s + 41.2 = vt = 4.6 t
Distance the bus moves = s = 1/2 * 0.163* t^2
1/2 * 0.163 * t^2 + 41.2= 4.6 t
t=11.16sec
2) For what distance does the student have to run at 4.6 m/s before she overtakes the bus?
student: s = 4.6m/s * t =4.6*11.16=51.34m
3) When she reaches the bus, how fast is the bus traveling?
Vbus = at = 0.163 * 11.16= 1.82 m/s
4) If the student's top speed is 3.00 m/s , will she catch the bus?
1/2 * 0.163 * t^2 + 41.2-4.6 t =0
t = (-b ± (b² - 4ac) ) / 2a
I think that at the minimum speed, that the discriminant will have a value of 0 so that t will have only one root (and not two). So b² = 4ac = 4(0.0815)(41.2) ======>b = 3.66 m/s
the speed must be 3.66m/s.
so, he can not catch th bus.
5) What is the minimum speed the student must have to just catch up with the bus?
3.66m/s (Answer in part 4)
6) For what time does she have to run in that case?
3.66t = 41.2 + 0.5*0.163t²
0.0815t^2-3.66t-41.2=0
Single root at t = 54.22s
7) For what distance does she have to run in that case?
s = 3.66m/s 54.22=198.44 m
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