1.) A particle starts from x o = 10 m at t o = 0 s and moves with the velocity g

Question

1.) A particle starts from xo = 10 m at to = 0 s and moves with the velocity graph shown.

a) describe what you would see if you were watching this particle as it moved.

b) Does the particle have a turning point? If so, at what time?

c) What is the object%u2019s position at t = 3 s?

d) What is the object%u2019s velocity at t = 3 s?

e) What is the object%u2019s acceleration at t = 3 s?  

2.) Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. A car traveling 105 km/h (65 mph) strikes a tree. The front end of the car compresses and the driver comes to rest after traveling 0.80 m.

Calculate the magnitude and duration of the acceleration during the collision.                                                                                                            

3.) You are driving down the road at 60 km/hr when you see a chicken dash out onto the road 23.3 m in front of you. After reacting, you slam on the brakes, and the car decelerates at 7 m/s2. The car stops just in time to avoid hitting the chicken. What was your reaction time? Solve using kinematics equations

Please show all equations and methods for solving!

Explanation / Answer

Deceleration distance s = at^2/2 = vt/2 = v^2/2a, so
a = v^2/(2s)
= 2275 m/s^2 for hardwood
= 360 m/s^2 for carpet
You could also have gotten about those same answers by continuing:
v = 2.94 m/s
t = 1.3 ms, a = v/t = 2262 m/s^2
t = 8.4 ms, a = v/t = 350 m/s^2

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