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VCE Stuff => VCE Science => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Physics => Topic started by: Srd2000 on January 31, 2019, 02:36:12 am

Title: Confusing Motion Problem
Post by: Srd2000 on January 31, 2019, 02:36:12 am

Hi All, I’ve got a rather confusing problem on my hands. I believe I’m over complicating it with velocity-time graphs and simultaneous equations, but I’m not sure.

A person walks 50km in 4hrs. They start off walking 7km at a rate of x km/h. Then they ride a bike at 4x km/h for another 7km. Lastly, they drive a car the remaining distance at (6x+3) km/h. What is the value of x km/h?

Ans: x=3.5 km/h

My intial thinking was to do a velocity-time graph and use the area as mentioned, but that fell short when I introduced t1 and t2, respective times for when the person changes their transport. Then I tried solving it simultaneously, that got a negative answer. I’m sure that I’ve just overthought it or gone down a rabbit-hole.

I’d much appreciate if someone could help out. Thank you!!!

Title: Re: Confusing Motion Problem
Post by: lzxnl on January 31, 2019, 03:42:13 pm

Quote from: Srd2000 on January 31, 2019, 02:36:12 am

Hi All, I’ve got a rather confusing problem on my hands. I believe I’m over complicating it with velocity-time graphs and simultaneous equations, but I’m not sure.

A person walks 50km in 4hrs. They start off walking 7km at a rate of x km/h. Then they ride a bike at 4x km/h for another 7km. Lastly, they drive a car the remaining distance at (6x+3) km/h. What is the value of x km/h?

Ans: x=3.5 km/h

My intial thinking was to do a velocity-time graph and use the area as mentioned, but that fell short when I introduced t1 and t2, respective times for when the person changes their transport. Then I tried solving it simultaneously, that got a negative answer. I’m sure that I’ve just overthought it or gone down a rabbit-hole.

I’d much appreciate if someone could help out. Thank you!!!

You know the total distance and total time. Use them.

First section: travels 7 km, 7/x hours
Second section: travels 7 km, 7/(4x) hours
Third section: 50 - 14 = 36 km, 36/(6x+3) hours
Add the times, set equal to 4 hours.

Title: Re: Confusing Motion Problem
Post by: Srd2000 on January 31, 2019, 05:31:37 pm

Oooooh, that makes sense. I kept trying to use just the distance and speed to find x while ignoring time completely. My bad, oops.

Thank you, lzxnl!