Can You Solve These Challenging Linear Motion Problems?

[Meamour]

Homework Statement

1) Harry Hopeless averages 40km/h for the first half of his car trip. How fast should he drive on the remaining half of the trip to have an average speed of 80km/h for his trip?
2) You drive to the city at an average speed of 40km/h and return at an average speed of 60kmh/ Find your average speed for the entire trip? Explain why the answer is not 50km/h
3)A train moves at a constant speed of 60Km/h toward a station 30km away. At that moment Fanny Fastbird leaves her perch on the locomotive and flies toward the station at a constant speed of 100km/h relative to the ground. When the bird reaches the station, she immediately turns around and flies back to the train at the same speed. What reaching the train she again immediately turns around and flies back to the station, repeating the process until the train passes the station. What total distance is traveled by the bird?
4) When Valerie VolleyBaller jumps to spike a ball, she rises a total of 2.0m in the air after accelerating through .5m (from crouch to full extension). What is her acceleration.

Homework Equations

Thanks to whoever took the time to read all that and try to help me. I have a beginner so I'd appreciate it if whoever answers can go step by step.
X= x0+v0t+at/2 X= Final position x0=Initial position v0=Initial Velocity/speed t=time a=acceleration
V=v0+at
V^2=v0^2+ 2a (x-x0)

The Attempt at a Solution

Out of 30 these were the 4 ones I couldn't do. I don't even know where to start. I'm very new to physics and my teacher isn't helping much.
Thank you!

 

[Simon Bridge]

The first three questions are all answered by knowing how to calculate average speed ... which is the total distance traveled, divided by the time it takes. $$\bar{v}=\frac{d}{T}$$

The last one requires a bit more work - so I'll deal with that last.
Please show me your attempt for each one.

 

[Meamour]

For the 1st one.. I was thinking since I don't have a distance.. could I just pick one? So I picked 100. V= 100/ t1+t2 Then t1= 50Km/40km/h= 5/4h but t2 would = 50/v2( what we are looking for, right? )
80=100/ 5/4h + 50/v2
80(5/4h+50/v2) = 100
5/4h+50/v2=100/80 (100/80 could be simplified to 5/4) and then we subtract 5/4 from both side and get
50/v2= 0 and that would be indefinite right?
2) I didn't know what to do without the distance or time, but I know that it is not 50km/h because both speeds don't have a constant acceleration, I looked at my relevant equations and still couldn't tackle the problem.
3)48 km?
4) I'm not sure where to start?
Thanks for the help!

 

[Simon Bridge]

For Q1: you can answer it right away without doing much math by considering what happens if the distance is 80 km. (If you must pick a number, and you can pick any you like, pick one that makes the math easy!)

Then, to average 80kmph, you'd have to do the whole trip in how long?
You've already done half the trip at 40kmph - how long have you been traveling already?
Compare with the total travel time needed.

This should help your confidence with your answer ;)

In general, though, you don't get to just invent numbers just because you are not given a number directly.
You would normally just leave anything you don't know as a variable.

Q2. You know that both distances are the same though, so it's like Q1.
Call that distance d.

The trick is to get used to using the math as a language to describe stuff.

if v₁=40kmph and the distance is d, then d=v₁T₁
Do the same for v2=60kmph ... and write another expression for the average speed v for the whole time T1+T2.

 

[Meamour]

So in Q1) the d is just a variable , and I would need to drive the whole trip in one hour to average 80km/hr... so in half the trip of 40km/hr.. that would take me 30 min. So would he need to drive 40km/hr to average? Because that is what I told my teacher and my teacher told me that I was wrong and the answer was impossible/indefinite. I didn't understand why he said that though.
Q2) So d/40+d/60= time. I would then make a common denominator and get 3d/120+2d/120 = 5d/120 , so isn't that going to be that the time = d/24?

 

[Simon Bridge]

I would need to drive the whole trip in one hour to average 80km/hr... so in half the trip of 40km/hr.. that would take me 30 min.

No. I suspect you are having trouble breaking a problem down into steps.
If the whole trip is 80km, how far is half the trip?
How long did it take to drive that distance at 40kmph?
To meet your goal (80kmph ave speed), the whole trip must take - how long?
Therefore - how much time is left for the rest of the trip?




for Q2: did it really take the same time to drive both legs of the journey?

 

[Meamour]

My internet was out, sorry it took me such a long time to reply, and thanks for being patient and helping me.
Q1) Half the trip is 40km, it took 30 minutes, i need to take 1 hour to average 80kmph , the rest of the trip is 40 minutes. Distance = Average * time, 80km= 80kmph * time.. so it would take me 1 hour... that's a no brainer but then Average speed = D/time but then I did 40kmph = 40/ time so time equals 1 hour so would half of the trip be 1 hour and the whole trip be 2 hours... I'm confusing my self. There is probably something I am missing?
Q2) v1t1 = D
40*t1=D so t1= D/40
V2t2=D
60*t2=D so T2= D/60 Total time = D/60 + D/40
D= D/ D/40 + D/60 right?
or would I use the equation V= Vi + at?

 

[Meamour]

I re-did Q1 and I got impossible! T= X/40 & T= X/R and D= 2x so D= 2x/80kmph ( R is what I am looking for)
X/40+ X/ R = 2x/80
so if I use 80 for my distance
2+ 80/R = 2
80/R = 0
80 = 0
and that's impossible! That's why his name was Harry Hopeless and my name isn't!

 

[Simon Bridge]

Half the trip is 40km, it took 30 minutes, i need to take 1 hour to average 80kmph , the rest of the trip is 40 minutes.

I have an issue with your reasoning there - you said you need to do the entire trip in 1 hour, you have already spent 30mins, therefore you have 40mins left? How many minutes are there in 1 hour?

Answer these questions in order and it will all become clear.

On the first half of the trip...
1. What speed were you doing?
2. How long is the first half of the trip?
3. How much time to do that distance at that speed?

Therefore:
4. How much time is left to complete the trip?