The earth moves around the sun in a nearly circular orbit of ra-dius 1.50 3 1011 m. during the three summer months (an elapsed time of 7.89 3 106 s), the earth moves one-fourth of the distance around the sun. (a) what is the average speed of the earth? (b) what is the magnitude of the average velocity of the earth during this period?

circumference of orbit = pi*1/2*1.5e11m = 2.356e11 meters
in 13 weeks, there are 13*7*24*60*60 seconds = 7.862e6 seconds
avg speed = 1/4*2.356e11meters/7.862e6sec = 0.07492e5 = 7.49e3m/sec

the avg velocity is 1.414* radius of the orbit

Answer: a charge of -1.0  × 10⁻⁴ c must be placed  at x = 26 m.the sign of the charge will be the same sign as the  -4.0  µc charge.======electricstatic force between two point charges  is given by    where k is coulomb's constant,  8.99×10⁹  n·m²/c², q₁ and q₂ are the point charges, and r is the distance between the two point charges.assign positive to q₁let q₁ =  6.0 µc, q₂ = -4.0  µc, q₀ represent the charge at the origin, and q₃ represent this new charge to place.the charge at the origin q₀ would experience the following force f₀₁ from q₁, with r = 6.0 m (note that 1  µc = 10⁻⁶ c)    the force from q₂    the force from q₃    the net force on the origin charge, q₀, has to be zero for no electrostatic forcehaving an equation where k and q₀ can be divided out of the equation will allow us to solve for q₃    isolating:     a charge of -1.0  × 10⁻⁴ c must be placed  at x = 26 m.the sign of the charge will be the same as the  -4.0  µc charge