College Physics| Openstax| Problem 2.39

In 1967, New Zealander Burt Munro set the world record for an Indian motorcycle, on the Bonneville Salt Flats in Utah, of 183.58 mi/h. The one-way course was 5.00 mi long. Acceleration rates are often described by the time it takes to reach 60.0 mi/h from rest. If this time was 4.00 s, and Burt accelerated at this rate until he reached his maximum speed, how long did it take Burt to complete the course? 

SOLUTION:

 

There are two parts to the race: an acceleration part and a constant speed part. First, we need to determine how long (both in distance and time) it takes the motorcycle to finish accelerating. During acceleration, a=\frac{600\:mph}{4\:s}.

v_{max}=at_1

t_1=\frac{v_{max}}{a}

t_1=\frac{183\:mph}{\left(\frac{60\:mph\:}{4\:s}\right)}

t_1=12.2\:s

x_1=v_{avg}t_1

x_1=\left(\frac{183\:mph+0\:mph}{2}\right)\left(12.2\:s\right)

x_1=\left(91.5\:mph\right)\left(\frac{1\:h}{3600\:s}\right)\left(12.2\:s\right)

x_1=0.31\:mi

At constant velocity, x_2=5\:mi-0.31\:mi=4.7\:mi.

Now, we complete the calculation by determining how much time is spent on the course at max speed.

t_2=\frac{x_2}{v_{max}}

t_2=\frac{4.7\:mi}{183\:mph}

t_2=\left(0.026\:h\right)\left(\frac{3600\:s}{1\:h}\right)

t_2=92\:s

So, the total time is

t_{total}=t_1+t_2

t_{total}=12.2\:s+\:92\:s

t_{total}=104\:s

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