1) A race car starts from rest and travels east along a straight and level track

Question

1) A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the car's motion, the eastward component of the car's velocity is given by x(t)=(0.920m/s^3)t^2.

a) What is the acceleration of the car when x = 12.9 m/s ?

Express your answer with the appropriate units.

2) The human body can survive a negative acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than 250m/s^2.

a) If you are in an automobile accident with an initial speed of 120 km/h and are stopped by an airbag that inflates from the dashboard, over what distance must the airbag stop you for you to survive the crash?

3) In the fastest measured tennis serve, the ball left the racquet at 73.14 m/s. A served tennis ball is typically in contact with the racquet for 32.0 ms and starts from rest. Assume constant acceleration.

a) What was the ball's acceleration during this serve?

b) How far did the ball travel during the serve?

Can you show the steps please. Thank you.

Explanation / Answer

a) 12.9 =0.92*t^2

t = 3.745sec

dv/dt = 2*0.92*t = 2*0.92*3.745 = 6.89m/sec^2

2) v^2-u^2=2as

here v=0

a is negitive

therefore 120kmph = 33.33mph

33.33^2 = 2*250*s

s = 2.2217 m

3) v=at

73.14/0.032 =a

2285.625 m/sec^2

b) 2*a*s =v^2

73.14^2 = 2*2285.625*s

s=1.17m

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