This is an example of an cumulation mulating the distances traveled over sho probleint in greater dead in Chapter 5. Finding Veloci The second fundamental quest of calcul it was not even clear what "velocity at a sing ocity when we know the pos sent" means. Velocity is distance tion at es moment, did not arise until almost ared years later. For a long time divided by time, so at a single moment, no diste has been traveled and no time ha elapsed! But we can look at velocities over short intervals of time close to the moment in question. Just as we were able to put upper and lower limits on distance, we can pu upper and lower limits on velocity near a given moment. To distinguish between the tra ditional understanding of velocity as distance divided by time and the concept of the velocity at a single moment, we refer to the total distance divided by the elapsed time a the average velocity. Exploration 2 Bounding the Velocity The Eagle X, a rocket designed to launch satellites into orbit, has height at time! seconds after lift-off that can be approximated by the function h(t) =1 1700(1 sin(t/200) 200 kilometers, 0 ≤ t≤ 120. t Kilometers 100 80 60 40 20 0 20 20 40 60 Seconds after lift-off 80 100 120 Time (sec) Height (km) 0 20 0 2.8 40 60 11.3 25.4 80 100 120 45.0 70.0 100.2 1. Is the rocket speeding up or slowing down over time? Use the data in the table to defend your answer. 2. We want to find bounds on the velocity at 60 seconds. Will the average velocity between the 60-second mark and the 80-second mark give us an upper bound or a lower bound on the velocity at 60 seconds? This is an example of an cumulation mulating the distances traveled over sho probleint in greater dead in Chapter 5. Finding Veloci The second fundamental quest of calcul it was not even clear what "velocity at a sing ocity when we know the pos sent" means. Velocity is distance tion at es moment, did not arise until almost ared years later. For a long time divided by time, so at a single moment, no diste has been traveled and no time ha elapsed! But we can look at velocities over short intervals of time close to the moment in question. Just as we were able to put upper and lower limits on distance, we can pu upper and lower limits on velocity near a given moment. To distinguish between the tra ditional understanding of velocity as distance divided by time and the concept of the velocity at a single moment, we refer to the total distance divided by the elapsed time a the average velocity. Exploration 2 Bounding the Velocity The Eagle X, a rocket designed to launch satellites into orbit, has height at time! seconds after lift-off that can be approximated by the function h(t) =1 1700(1 sin(t/200) 200 kilometers, 0 ≤ t≤ 120. t Kilometers 100 80 60 40 20 0 20 20 40 60 Seconds after lift-off 80 100 120 Time (sec) Height (km) 0 20 0 2.8 40 60 11.3 25.4 80 100 120 45.0 70.0 100.2 1. Is the rocket speeding up or slowing down over time? Use the data in the table to defend your answer. 2. We want to find bounds on the velocity at 60 seconds. Will the average velocity between the 60-second mark and the 80-second mark give us an upper bound or a lower bound on the velocity at 60 seconds?