In the soapbox Derby, young participants build non-motorized cars with very low friction wheels. Cars race by rolling down a hill. The track at Akron’s Derby Downs, where the national championship is held, begins with 55-ft  long section tilted 13° below horizontal.

a) What is the maximum possible acceleration of a car moving down this stretch of track? 

 

F_net= F_gravity
=> a_max = m_gravity  x  sin(13)
=>a_max = 9.8 x 0.22

= 2.20 m/sec²

 

b) If a car starts from rest and undergoes this acceleration for the full l, what is its final speed in m/s?

55 feet converted to meters = 16.76 meters

v² = u² + 2as
=>v² = 0 + 2 x 2.20 x 16.76
=>v = √ (73.74)

= 8.59 m/s