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An airplane starts from rest, travels 5000 ft down a runway, and after uniform acceleration, takes off with a speed of 162 mi/h. It then climbs in a straight line with a uniform acceleration of 3 ft/{ s }^{ 2 } until it reaches a constant speed of 220 mi/h. Draw the st, vt, and at graphs that describe the motion.

Step-by-step

{ v }_{ 1 } = 0 \\ { v }_{ 2 } = 162 \frac { mi } { h } \frac { (1h) 5280ft } { (3600s) (1mi) } = 237.6 ft/s \\ { v }_{ 2 }^{ 2 } = { v }_{ 1 }^{ 2 } + 2 { a }_{ c }({ s }_{ 2 } – { s }_{ 1 }) \\ { (237.6) }^{ 2 } = { 0 }^{ 2 } + 2({ a }_{ c })(5000 – 0) \\ { a }_{ c } = 5.64538 ft/{ s }^{ 2 } \\ { v }_{ 2 } = { v }_{ 1 } + { a }_{ c }t \\ 237.6 = 0 + 5.64538 t \\ t = 42.09 = 42.1 s \\ { v }_{ 3 } = 220 \frac { mi } { h } \frac { (1h)5280 ft } { (3600 s)(1 mi) } = 322.67 ft/s \\ { v }_{ 3 }^{ 2 } = { v }_{ 2 }^{ 2 } + 2{ a }_{ c }({ s }_{ 3 } – { s }_{ 2 }) \\ { (322.67) }^{ 2 } = { (237.6) }^{ 2 } + 2(3)(s – 5000) \\ s = 12 943.34 ft \\ { v }_{ 3 } = { v }_{ 2 } + { a }_{ c }t \\ 322.67 = 237.6 + 3 t \\ t = 28.4 s

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