Calculating Acceleration and an Algebra 1 problem

Question

I need help on these problems regarding acceleration:

 

1. The head of a rattlesnake can accelerate at 50.0 m/s^2 in striking victim. If a car would have the same acceleration, how long would it take for it to reach a speed of 100.0 km/h from rest? ( First we need to figure out how many m/s 100 km/h is equal to.)

 

2. A soccer player, running at 3.2 m/s, decides to accelerate. For the next 6.0 s, he speeds up with an acceleration of 0.50 m/s^2. What is his speed at the end of the run? 

 

3. a. A windmill-style softball pitcher executes a pitch in 0.65 seconds. The ball accelerates from 0 m/s           to 40 m/s. What is the acceleration?

    b. Convert 40 m/s to mi/h. What is the acceleration in the above problems in mi/h/s?

 

And I also need help with this problem relating to quadratic equations and their discriminant:

 

1. For any quadratic equation ax^2+ bx+ c= 0, the sum of the solutions equal to -b/a, and the product of the solutions is equal to c/a. Show that this is true for x^2 - x - 6 = 0.

Answer 1

X ^2 - X -6  =  X^2 +2X - 3X - 6

                  = X ( X +2 ) - 3 ( X + 2) = ( X -3 ) ( X +2 )

 

   X^2 - X - 6 = 0 , then    ( X - 3 ) ( X +2 ) =0

 

    X - 3 = 0   X₁ = 3    X + 2 = 0  X₂ = -2

 

  X ^2  - ( X₁ + X_{2 )} X  + X_1. X_{2 = X ^2 - ( 3 - 2 ) X + 3 ( -2) = X^2 - X - 6}