TCO 2 This question requires a numeric or algebraic answer I

(TCO 2) This question requires a numeric or algebraic answer. In order to receive full credit for this problem, you must show all your work. To show your work for this problem, you may scan neatly handwritten work or type up your work in MS Word using the equation editor and submit it using the Midterm Dropbox. You should make your submissions after you complete the exam. David is driving at a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s2 at the instant when David passes. How far does Tina drive before passing David? What was her speed as she passed him? (Points : 20)

Solution

initial velocity of David,

u1 = 30 m/s

initial velocity of Tina:

u2 = 0

acceleration of Tina, a = 2 m/s2

Let the distance traveled by Tina before she passes David be s,

So, using equation of motion,

s = ut + 0.5*at^2

For Tina:

u = 0

a= 2 m/s2

So, s = 0.5*2*t^2

Now, in this amount of time t, distance traveled by David :

s = 30*t

So, s = 30*t = 0.5*2*t^2

So, 30*t = t^2

So, t = 30 s

So, distance traveled by Tina = 0.5*2*30^2 = 900 m <------answer