Datasets:
raphassaraf
/
MNLP_M3_rag_dataset_withdocs

Dataset card Data Studio Files
xet
Community
1
source
string
id
string
question
string
options
list
answer
string
reasoning
string
AQUA-RAT
AQUA-RAT-39997
# Physics kinematics SIN question 1. Dec 30, 2011 ### ShearonR 1. The problem statement, all variables and given/known data A car, travelling at a constant speed of 30m/s along a straight road, passes a police car parked at the side of the road. At the instant the speeding car passes the police car, the police car starts to accelerate in the same direction as the speeding car. What is the speed of the police car at the instant is overtakes the other car? Given: v=30m/s vi=0 Need: vf=? 2. Relevant equations vf=vi+αΔt vf2=vi2+2αΔd v=Δd/Δt 3. The attempt at a solution So far, I really have not gotten anywhere. I believe what I have to do is somehow manipulate the velocity equation of the first car into something I can input into the vf equation for the police car. I have been having much trouble with this question and would appreciate any tips to point me in the right direction. 2. Dec 30, 2011 ### Vorde This isn't solvable without knowing the acceleration of the police car, without it the velocity when the police car overtakes the other car could be anything. edit: You don't necessarily need the acceleration, but you need at least one other piece of information (such as at what distance did the police car overtake the other car) to solve the problem. 3. Dec 30, 2011 ### ShearonR Yes, and that is what I have been fretting over this whole time. They give multiple choice answers, but essentially they all work. I know that depending on the magnitude of the displacement or the time, the rate of acceleration will change. 4. Dec 30, 2011 ### Staff: Mentor Interesting. I think I was able to solve it just with the given information (unless I did something wrong). Pretty simple answer too. You should write an equation that equates the distance travelled to the meeting/passing spot for each car (call that distance D). The speeding car's velocity is constant, so what is the equation for the time it takes for the speeding car to get to D? The following is multiple choice question (with options) to answer. Liam is pulled over for speeding just as he is arriving at work.He explains to the police officer that he could not afford to be late today, and has arrived at work only four minutes before he is to start. The officer explains that if Liam had driven 5mph slower for his whole commute, he would have arrived at work exactly on time. If Liam's commute is 20 miles long,how fast was he actually driving?(Assume that Liam drove at a constant speed for the duration of his commute.)
[ "40 mph", "45 mph", "48 mph", "52 mph" ]
A
Let t be the number of hours he would need to reach office on time. when he is driving with over speed, he reached office 4 min earlier! so the equation for this is s(t - 4/60) = 30 where s is the speed and 30 is the distance. if he decreases his speed by 5mph then he would have reached his office on time: (s-5)t = 30 if you solve above equations, you will arrive at t = 2/3 hr and s = 40mph therefore answer is A
AQUA-RAT
AQUA-RAT-39998
5. Hello, James! Another approach . . . 12 Students are in a class. Five can go to room A, Four to room B, and Three to room C. How many ways can this happen? Assign 5 students to room A. . . There are: . $_{12}C_5 \:=\:\frac{12!}{5!7!} \:=\:792$ ways. From the remaining 7 students, assign 4 students to room B. . . There are: . $_7C_4 \:=\:\frac{7!}{4!3!} \:=\:35$ ways. From the remaining 3 students, assign 3 students to room C. . . Of course, there is: . $_3C_3 \:=\:1$ way. Therefore, there are: . $792 \times 35 \times 1 \:=\:27,\!720$ ways. The following is multiple choice question (with options) to answer. The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?
[ "72", "55", "44", "66" ]
A
Sum of the marks for the 12 students = 12 * 36 = 432. The marks of each student are doubled, the sum also will be doubled. The new sum = 432 * 2 = 864. So, the new average = 864/12 = 72. Answer: A
AQUA-RAT
AQUA-RAT-39999
homework-and-exercises, kinematics Title: Average Velocity A car travels 100 miles in 2 hours, it then completes the return leg of the journey. How fast must it travel on the return leg to average 100mph over the total journey. My thoughts on this are that it is impossible as if the total average was 100mph then the total time would be 2 hours but that can't be if the first leg took 2 hours. Please tell me if I am missing something Are you missing something? You probably are if this question was asked during a course on relativity. Anyway, this is a physics site and I'm going to make the question a bit more precise on the reference frames in which the measurements might have taken place: We observe a car travel 100 miles in 2 hours, it then completes the return leg of the journey. How fast must it travel on the return leg for the driver to have done the full 200 miles in 2 hours? The answer starts from the observation that during the first leg the driver will have aged $2\sqrt{1-\frac{v^2}{c^2}}$ hours, with $v/c \approx 50/670616629 \approx 7.5 \ 10^{-8}$. That is a fraction $5.6 \ 10^{-15}$ short of 2 hours. So, the second leg the car should travel at a speed $v'$ such that the driver ages $\sqrt{1-\frac{v'^2}{c^2}} \frac{100 mi}{c}= 11 \ 10^{-15}$ hr. It follows that $v'$ needs to be a fraction $3 \ 10^{-15}$ short of the speed of light. The following is multiple choice question (with options) to answer. A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 6 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?
[ "(a) 24/5", "(b) 6", "(c) 26/5", "(d) 27/5" ]
B
from the uphill we can find out the distance = 6*2 = 12 average speed = total distance/total time = 24/ (2+ (12/6)) = 6 Answer is B.
AQUA-RAT
AQUA-RAT-40000
Sol: Folks, look at the relative calculation here. If we consider that all the 120 candidates passed the examination, the average of the entire class must be 39. But it is given that average of the entire class is 35. So we are getting an extra of 4 in the average i.e. an extra of 4x120=480 in the total sum. We got extra total sum because some students who failed were also considered to be passed. For every one student considered as passed who actually failed we get 39-15 = 24 marks extra. Since we got 480 marks extra, total number of failed students who were considered as passed = 480/24 = 20. Hence the total number of students who passed = 100 You can solve this by assuming that all the 120 failed the examination but this would take a bit extra time. Folks, most of the questions solved here can also be solved quickly by using a technique called Alligation. I will soon come up with a tutorial on this topic and I will discuss these questions in that tutorial besides some other questions as well. So stay tuned.... _________________ Manager Joined: 22 Feb 2009 Posts: 140 Schools: Kellogg (R1 Dinged),Cornell (R2), Emory(Interview Scheduled), IESE (R1 Interviewed), ISB (Interviewed), LBS (R2), Vanderbilt (R3 Interviewed) Followers: 8 Kudos [?]: 79 [1] , given: 10 Re: Average Accelerated: Guide to solve Averages Quickly [#permalink]  19 Apr 2009, 21:07 1 KUDOS cicerone wrote: Problem 5: The average of batsmen up to certain number of innings was 45. In the next inning he was out for a duck and his average reduced to 40.5. Find the total number of innings played by him including the latest inning. Sol: Again, if the batsmen had scored 45 in his latest inning his average would remain in tact i.e. it would have been 45. But he scored 0 runs. Since he did not score 45, he lost an average of 4.5 upon the total number of innings, which includes the latest innings as well. So 45 runs upon x innings will give an average of 4.5 The following is multiple choice question (with options) to answer. A student got 72% in math and 84% in history. To get an overall average of 75%, how much should the student get in the third subject?
[ "65%", "67%", "69%", "71%" ]
C
72 + 84 + x = 3*75 x = 69 The answer is C.