In September 2003, Tony Schumacher started from rest and drovea quarter mile (13

Question

In September 2003, Tony Schumacher started from rest and drovea quarter mile (1320 ft) in 4.498 s in a national hot rodassociation race. His speed as he crossed the finish line was328.54 mph. Assume that the car's acceleration can be expressed bya linear function of time a = b + ct. (a) Determine the constants b and c (b) What was the car's speed 2sec after the start of therace? In September 2003, Tony Schumacher started from rest and drovea quarter mile (1320 ft) in 4.498 s in a national hot rodassociation race. His speed as he crossed the finish line was328.54 mph. Assume that the car's acceleration can be expressed bya linear function of time a = b + ct. (a) Determine the constants b and c (b) What was the car's speed 2sec after the start of therace?

Explanation / Answer

S = 1320 ft, T = 4.498 s, V = 328.54 mph = 481.86 ft/s a = b + ct v(t) = a dt = bt + ct2/2 so V = bT +cT2/2            (1) s(t) = v dt = bt2/2 + ct3/6 so S = bT2/2 +cT3/6        (2) solve (1) and (2), and get b = 2(3S - VT)/T2 = 177.2 ft/s2 c = 6(VT - 2S)/T3 = -31.16 ft/s3 v(2) = b*2 + c*22/2 = 292 ft/s = 199 mph

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