If a ball is thrown in the air with a velocity 48 ft/s, its height in feet t seconds later is given by y = 48t (a) Find the average velocity for the time period beginning when t = 2 and lasting (i) 0.5 second. (ii) ft/s 0.1 second. ft/s (iii) 0.05 second. ft/s (iv) 0.01 second. ft/s (b) Estimate the instantaneous velocity when t = 2. ft/s 16t².

A car's position in feet t seconds after it starts moving is given by s(t)-9t/t. The average rate of change in position with respect to time is called average velocity %3D ) Find the car's average velocity over the first 4 seconds. DO NOT INCLUDE UNITS WITH YOUR ANSWER. i) Find the car's average velocity from t = 16 to t = 25 seconds. DO NOT INCLUDE UNITS WITH YOU ANSWER. i) What units would your answers from parts i and ii be in? O A. feet O B. feet per second OC. seconds O D. seconds per foot per foot O E. feet per second per second OF. seconds per foot

A rocket has taken off and is rising vertically according to the position equation, s = 50t^2 (use this to find the “given” rate of change). It is being tracked by a device located 2000 ft from the point of lift-off. The angle θ (in radians) is the angle between the tracking line and the ground. Find the rate of change in the angle θ , 10 seconds after lift-off.(a) GIVEN: Use the position function to find the given rate of change at t = 10 sec.(b) FIND: Write the derivative you want to find.(c) Write an equation relating the variable θ and two sides of the triangle. Then, differentiate with respect to time. (d) Solve for the unknown derivative in (b) after substituting in known values. Note: first you will need to solve for both s and the length of the hypotenuse at t = 10 sec.. Use a calculator for your final computations.

A person is walking at a rate of 5 ft per hour toward the foot of a flag pole 60 feet high. At what rate is the distance S(x) from the head of the person to the top of the pole changing when 80 ft from the bottom of the flag pole?