Questions asked by Vasilis R.

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• A resting car starts accelerating with #α=5.0m/s^2# , then uniformly, and finally, decelerating at the same rate, #α#, comes to a stop. The total time of motion equals #t=25s#. The average velocity is #72# kmph. For how long does the car move uniformly?
  
• A train previously at rest starts accelerating. It takes 4 seconds for the first carriage to cross the reference point K. How long will it take for the 10th carriage to cross the same point? (All carriages are the same width)
  
• A resting car starts accelerating with a = 5.0 m/s^2, then it goes uniformly, and finally, decelerates at the same rate (a) and comes to a stop. The total time of motion equals t = 25 s. The average velocity is v= 72 kmph. How long does it move uniformly?
  
• The velocity of a particle moving in the positive direction of the x axis varies as v= a*#sqrt(x)#, where a is a positive constant. Assuming that at the moment t = 0 the particle was located at the point x = 0, find the time dependence of the velocity?
  
• A car drives one fourth of a road with u_1 the next fourth with u_2 the next with u_3 and the final with u_4. what is the average speed?
  
• A body of mass M is falling from a very high building. The drag force is given by F=kv^2 where k is a constant and v its velocity. How soon will it reach terminal velocity and what will the distance traversed be equal to?
  
• The distance between two objects with mass m1 and m2 are in the intergalactic space is equal to l. With no other forces acting except gravity, how soon will they collide?
  
• From a height H, I shoot horizontally a ball(a) (mass M), while I drop another ball (b) with mass (2M). The initial speed of ball (a) is half of the max speed of ball(b). What is the ratio |Δp(a)|/|Δp(b)| over the whole time of motion?
  
• A boat mass M and I fill it up with fuel mass m. When it moves with velocity υ the resistive force is F=kυ^2. 1kg of fuel gives λ Joules of energy*. How much fuel (kg) is needed to sail d meters? *Suppose no energy is lost.
  
• On a surface I have two point charges Qa and Qb, 1C and 4C respectivly and are placed at A(-3,0) B(3,0). Find all the points (locus) (except those that are too far away) where V=0.?
  
• I flip a coin 10 times and I get 8 heads. what the propability of the 11th flip to be tails?
  
• I roll a 6sided dice twice. What the propability to get the same number twice?
  
• Rope of length 80m and mass M is connecting two rods 50 meters high. The minimum distance of the curve from the ground is 10 meters. How far are the two rods apart?
  
• #e^x#+#lnx#+#2x#=#3# Find all possible values of x.?
  
• #lim(x->0)# sin(x)*sin(#1/x#) solve the limit?
  
• Find sin72 if you know the sines of 30 45 60?
  
• #2^x#+#3^x#=#5^x# find all possible values of x?
  
• A resting car starts accelerating uniformly at #a_1# rate a then moves at a constant velocity =4m/s then decelerates at a constant rate #a_2#. the velocity of the car is greater than 2m/s for 10sec. What is the distance traversed by the car?
  
• A yo-yo is made of 3 disks (same material) and the inner one is 3times smaller than the two outer ones (R/r=3). A string (small thickness) is wrapped around the center disk. What will its acceleration be equal to?
  
• Find possible answers to the following differential equation #ddotx+κx=0#?
  
• #A=1+1/{1+1/[1+1/(1+1/...)]}# by solving it i get both a positive and a negative solution. Why negative?
  
• #2f((x-2)/(x+1))+f((x+1)/(x-2))=x# Find #f(x)#?