In the Soapbox Derby young participants build nonmotorized c

In the Soapbox Derby, young participants build non-motorized cars with very low-friction wheels. Cars race by rolling down a hill. Assume that the track begins with a

53-ft-long (1 m = 3.28 ft) section tilted 14 below horizontal.

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

Express your answer to two significant figures and include the appropriate units.

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

Express your answer using two significant figures.

Solution

maximum possible acceleration is gsintheta since that is the component of gravity along the inclined surface

hence acceleration = gsintheta = 9.8*sin14 =9.707m/s^-2

to find speed, use

v^2=u^2+2as

v=final velocity
u=initial velocity =0
a=accel = 9.707m/s^-2
s=distance =53 feet = 16.15m

v^2=0^2+2*9.7*16.15
v =17.70 m/s
solve for v (I get 17.70m/s)