. A car leaves Seattle heading east. The speed of the car in mph after m minutes

Question

. A car leaves Seattle heading east. The speed of the car in mph after m minutes is given by the function C(m) = 70m2/10 + m2 .

(a) Find a function m = f(s) that converts seconds s into minutes m. Write out the formula for the new function C(f(s)); what does this function calculate?

(b) Find a function m = g(h) that converts hours h into minutes m. Write out the formula for the new function C(g(h)); what does this function calculate?

(c) Find a function z = v(s) that converts mph s into ft/sec z. Write out the formula for the new function v(C(m); what does this function calculate?

Explanation / Answer

C(m) = 70m^2/(10 + m^2) where m is minutes

a) m =f(s);

m= s/60

Now C(f(s) is found by plugging m= f(s) =60s

C(f(s)) = 70(s/60)^2/( 10 +(s/60)^2)

= 70s^2/( 36000 +s^2) .The function calculates speed of car after s seconds

b) m =g(h); m= h*60 =60h

Plug m= 60h in C(m) ;

we get C(g(h)) = 70(60h)^2/( 10 + (60h)^2 )

= 70*3600h^2/( 10 + 3600h^2)

This function calculates in term of hours

c) 1 mph = 1.467 ft/sec

s = 1.467z ; z =0.681s

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