When we estimate distances from velocity data it is sometimes necessary to use times $t_0,t_2,t_2,t_3,$dots, that are not equally spaced. We can still estimate distances using the time periods $t_i=t_i-t_{i-1}.$ For example, on May $7,1992,$ the space shutte Endenrour wan launched on mission STS$-49,$ the purpose of which was to install a new perigee kick motor in an Intelsat commanications satellte. The table provided by NASA, gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters.

$\backslash$table$[[$Event$,$Time $(a),$Velocity $($ft$/$s$)],[$Launch$,0,0],[$Begin roll maneuver,$10,185],[$End roll maneuver,$15,319],[$Throttle to $89$ percent,$20,447],[$Throttle to $67$ percent,$32,742],[$Throttle to $104$ percent,$59,1325],[$Maximum dynamic pressure,$62,1445],[$Solid rocket booster separation,$125,4151]]$

Use these data to estimate the height $($in feet$)$ above Earth surface of the space shuttie Endeerear, $62$ seconds aller instt in your estimate, use right endpoints.

Height at $62$ seconds after takeoff n $$ feet