EXAMPLE 2.6 Runway Length Origin Goal Apply kinematics to horizontal motion with two phases. +x coasting i distance braking distance Problem A typical jetliner lands at a speed of 160 mi/h and decelerates at the rate of (10 V% = 71.5 m/s a = 0 t = 1.0 s vo = 71.5 m/s mi/h)/s. If the plane travels at a constant speed of vy = 0 a =-4.47 m/s2 160 mi/h for 1.0 s after landing before applying Coasting and braking distances for a landing jetliner. the brakes, what is the total displacement of the aircraft between touchdown on the runway and coming to rest? Strategy First, convert all quantities to SI units. The problem must be solved in two parts, or phases, corresponding to the initial coast after touchdown, followed by braking. Using the kinematic equations, find the displacement during each part and add the two displacements. SOLUTION 0.447 m/s Convert units of speed and acceleration vo = (160 mi/h) = 71.5 m/s 1.00 mi/ h ) to SI. 0.447 m/s (-10 (mi/h)/ s)( 1.00 mi/ h ) = -4.47 m/s2 0, vo = 71.5 m/s, and t = Taking a = vot + V2at? = (71.5 m/s)(1.00 s) + 0 = 71.5 Ax coasting %3D 1.00 s, find the displacement while the plane is coasting. v2 = vo? + 2aAxbraking Use the time-independent kinematic %3D equation to find the displacement while the plane is braking. 0 - (71.5 m/s)? - vo Take a = -4.47 m/s and vo 71.5 Axbraking -= 572 m 2a 2.00 (-4.47 m/s²) m/s. The negative sign on a means that the plane is slowing down. 644 m = 72 m +572 m = Sum the two results to find the total Ax coasting + Axbraking displacement. LEARN MORE Remarks To find the displacement while braking, we could have used the two kinematics equations vot + V2 at? and v = vo + at, but because we weren't interested in time, the involving time, namely, Ax time-independent equation was easier to use. Question By how much would the answer change if the plane coasted for 2.0 s before the pilot applied the brakes? 571.85 PRACTICE IT Use the worked example above to help you solve this problem. A typical jetliner lands at a speed of 147 mi/h and decelerates at the rate of (10.2 mi/h)/s. If the jetliner travels at a constant speed of 147 mi/h for 1.5 s after landing before applying the brakes, what is the total displacement of the jetliner between touchdown on the runway and coming to rest? 571.85 EXERCISE HINTS: GETTING STARTED I I'M STUCK! A jet lands at 39.7 m/s, applying the brakes 1.67 s after landing. Find the acceleration needed to stop the jet within 5.42 × 102 m. m/s? -1.65 Need Help? Talk to a Tutor