A silver dollar is dropped from the top of a building that is 1367 feet tall. Use the position function below for free-falling objects. s(t) = −16t2 + v0t + s0 (a) Determine the position and velocity functions for the coin. s(t) =        v(t) =        (b) Determine the average velocity on the interval [1, 2].  ft/s (c) Find the instantaneous velocities when t = 1 second and t = 2 seconds. v(1) =  ft/s v(2) =  ft/s (d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.) t =  s (e) Find the velocity of the coin at impact. (Round your answer to three decimal places.)  ft/s

Q: The deck of a bridge is suspended 295 feet above a river. If a pebble falls off the side of the…

A:

Q: A particle moves along a straight line and has acceleration given by s" = 5t. Its initial velocityis…

A:

Q: Find the velocity of a particle when  S = t2 + 3t - 4 at t = 1 sec

A:

Q: Find the maximu rate of change of the function f(x y) = x² + xy + y² at the point (6, 7). O 386 V653…

A: →Maximum rate of change of function is along gradient, which is given by,               ∇f(x,y) =…

Q: The displacement (in meters) of a particle moving in a straight line is given by s = t2 - 8t + 17,…

A: We have solve the problem by putting the value of interval in average velocity formula.

Q: If a space shuttle's downward acceleration is given by y"(t) = –32 ft/s², find the osition function…

A:

Q: The deck of a bridge is suspended 205 feet above a river. If a pebble falls off the side of the…

A: Given, y= 205-16t² (height) We know that, Average velocity is given by, Average velocity=…

Q: If a ball is thrown into the air with a velocity of 40 ft/s its height in feet t seconds later is…

A: The height of the ball after t seconds is y=40t-16t2 (a)(i) Average velocity of the ball for the…

Q: If a ball is thrown straight up into the air with an initial velocity of 50 ft/s, it height in feet…

A:

Q: For function f (x, y) y? x²+1 Find the maximum rate of change of f at the point (1, 2)

A:

Q: a particle moves according to the function s(t)= t^2 - 2t +5,  what is the instantaneous velocity of…

A: A particle moves according to the function s(t)=t2-2t+5

Q: Find velocity (f'(x)) and acceleration (f''(x)) at time or t=0 with equation s(t)=2((e^t)-(e^-t))

A: We have to find velocity and acceleration

Q: For the graph y = f(x) = 3x² – x + 2 (i) (ii) Q3. %| - Find the average rate of change of y w.r.t x…

A:

Q: If a ball is thrown in the air with a velocity 48 ft/s, its height in feet t seconds later is given…

A:

Q: B2(a): Using the definition of derivative, find the derivative of f(x) = x² + 8. B2(b): The position…

A: (a).   From the given problem:   fx=x2+8   Now use the definition of derivative:…

Q: If a ball is thrown in the air with a velocity 42 ft/s, its height in feet t seconds later is given…

A:

Q: Let v(t) = t2 -2t-5 be the velocity function for a particle moving along a straight line. Here,…

A:

Q: The displacement (in meters) of a particle moving in a straight line is given by s = t2 – 5t + 15,…

A: Given: s=t2-5t+15, where t is measured in seconds

Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = 3t2 – 60t.…

A: v(t)=3t2-60t,    t≥0the particle is moving to the right whenv(t)>03t2-60t>03t(t-20)>0

Q: At time t ≥ 0, the velocity of a body movingalong the horizontal s-axis is v = t2 - 4t + 3. When is…

A: Given velocity of a body:

Q: At time t=0, a driver jumps from a diving board that is 25 feet high. Because the drivers initial…

A: Given, Position function, h(t) = -16t2+15t+25 a) When the diver hit the water, h(t)=0…

Q: Show that for an object falling according to Galileo’s formula, the average velocity over any time…

A:

Q: If a baseball is thrown upward with a velocity of 45 m/s, its height in meters t seconds later is…

A: We know that, Average velocity          = change in position/time elapsed.

Q: (a) Find the average velocity for the time period beginning when t = 2 and lasting for each of the…

A:

Q: The velocity of a particle moving along a line is given by v(t)=t^3−4t^2 meters per second. Find the…

A: To find the displacement of the particle, velocity should be integrated w.r.t. time.

Q: 4) For the function p = x2y+ yz at the point (1,2,-1), find its rate of change with distance in the…

A: Given data: Function:

Q: Q4: Find the derivative of the function at Po in the direction of A 1) f(x, y) = 2.xy -3y, P.(5,5).…

A:

Q: The position function of a particle is given by s(t) = 3t2 – t3, t > 0. (a) When does the particle…

A: The given position function is:  s(t)=3t2-t3So, the velocity function…

Q: Sketch the graph of y = v4-x², - 2<x<2. a

A:

Q: If a ball is thrown into the air with a velocity of 40ft/s, its height in feet t seconds later is…

A: The ball is thrown into the air with a velocity of 40ft/s, its height in feet t seconds later…

Q: (b) If a rock is thrown upwared on the planet mars with a velocity of 12ms, its height in meters t…

A: The height of the rock is given by: y(t)=12t-1.92t2 To find the average velocity over the interval…

Q: nen does the particle reach a velocity of 137 m/s if its position function is given by:…

A:

Q: Suppose a stone is dropped from a height of 200 ft. Its position at time t is s(t) =-12r +200. Find…

A: To find the time t when instantaneous velocity equal to average velocity.

Q: The altitude of a helicopter at three different instants is listed as below: 0.2 445.98 0.45 t, sec…

A: We will start by using formula for derivative by 1st principle

Q: The deck of a bridge is suspended 215 feet above a river. If a pebble falls off the side of the…

A:

Q: The velocity function (in meters per second) is given by v(t) = t2 - 2t - 3, for a particle moving…

A: We will use formula for the Displacement and distance in terms of Velocity function

Q: The position function of a particle is given by s(t) = 3t2 - t°, t 2 0. (a) When does the particle…

A: This question is based on derivative application.

Q: the supply function for luminar lamps is p=0.1x2+o.5x+15, where x is measured in thousands of lamps…

A: Given: A supply function for luminar lamps p=0.1x2+0.5x+15, where p is the unit price in dollars and…

Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t² -…

A: We have a particle moving along a horizontal line such that its velocity in m/sec is given by…

Q: If a rock is thrown upward on the planet Mars with a velocity of 12 m/sec, its height (in meters) t…

A:

Q: f a ball is thrown into the air with a velocity of 40 ft/s, its height in feet t seconds later is…

A:

Q: A particle moves along a straight line so that after t (seconds), its distance from Oa fixed point…

A:

Q: The velocity function of a particle moving along a horizontal line is given by yt) = t? – 8t + 15,…

A:

Q: The displacement (in meters) of a particle moving in a straight line is given by s = t2 – 3t + 10…

A:

Q: Q1) Find the tangent y = vx² – x + 7 at x = 2.

A: The detailed solution is as follows below:

Q: At time t ≥ 0, the velocity of a body movingalong the horizontal s-axis is v = t2 - 4t + 3. When is…

A:

Q: Q1. A particle moves along a straight line so that after t (seconds), its distance from O a fixed…

A: A particle is moving along the straight line so that it's distance from a fixed point 'O' after time…

Q: If a ball is thrown in the air with a velocity 50 ft/s, its height in feet t seconds later is given…

A: If a ball is thrown into the air with a velocity of 50 ft/s, its height in feet t seconds later is…

Q: At time t seconds, the center of a bobbing cork is 2sin(2t) centimeters above or below water level.…

A: ft=2sin2t Now velocity is the derivative of position with respect to time. So differentiating…