An alien on another planet throws a ball is thrown into the air. Its height (in feet) after t seconds is given by f(t)=51t−14t^2. Find the average velocities, Round to 3 decimal places.  The average velocity between 1.4 and 2.4 seconds, between 3.9 and 4.4 seconds.  Find the instantaneous velocity at 1 second.

Q: A deep sea divingbell is beinglowered ata constant rate. After 11 minutes, the bell is at adepth of…

A: We have to find the average rate of lowering per minute. For that we need to determine the change in…

Q: Find the rate of change of the distance D from the origin of a point moving on the graph of f(x) =…

A:

Q: A particle moves in a straight line with velocity t-2-25 ft/s. Find the total displacement and total…

A: v(t)=(1/t^2)-1/25

Q: Suppose a migrating bird flies at a constant altitude of 5 km, with a velocity of 42 km/h. At time t…

A: Given that, A migrating bird flies at a constant altitude of 5 km, with a velocity of 42 km/h. At…

Q: pnd inkgal. the indefinie 10 (x H10

A: By substitution, we calculate the given integral.

Q: a.)A construction worker dropped his laptop off the top of a high-rise office building. The height,…

A: A construction worker dropped his laptop off the top of a high-rise office building. The height,  in…

Q: You are on a trip, and at time point t=3.1t=3.1 your tripmeter (the meter that tells you how many…

A:

Q: The rock hits the surface after 5.38 seconds. With what velocity will the rock hit the surface?

A: Given H=15t-2.79t2 Velocity can be obtained with  differentiation of height. V=dH/dt

Q: The radius of a cylinder is increasing at a constant rate of 2 inches per minute. The volume remains…

A:

Q: The length of a rectangular box is increasing at 3 in/sec, while its width is decreasing at 4…

A: Differentiate volume of rectangular box wrt t

Q: Find the rate of change of the distance D from the origin of a point moving on the graph of f(x) =…

A:

Q: A rectangular water tank is being filled at the constant rate of 28 cubic meters per second. The…

A: Given information dVdt=28 m3/second Dimension w=2 meter and L=4 meters We have o find the rate of…

Q: You are lying on the beach watching a balloon float upward at a rate of 2 meters/sec from a point 50…

A: The balloon floats upwards at a rate of 2 meters/sec. The upward distance traveled after t seconds =…

Q: The radius of a spherical balloon is increasing at a rate of 4 centimeters per minute. How fast is…

A:

Q: During each cycle, the velocity (v in mm/s) of a piston is v=18t−18t^2, where t is the time in…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.