a weight is bouncing up and down on a spring with height h(feet) after t seconds, given by h(t)= 32sin(t/2) + 50. at which time is the acceleration of this weight approximately equal to -4 ft/s

Q: Find the acceleration a(t) of a ball tossed vertically in the air from ground level with an initial…

A: When the ball is tossed up, the ball with initial velocity of 12m/s will start decelerating and will…

Q: A poplulation of 500 bacteria is introduced into a culture and grows in number according to the…

A: The growth of the population of 500 bacteria is given by the equation

Q: A proton moves in an electric field such that its acceleration (in cm s-²) is given by: 40 a(t) (4t+…

A:

Q: Suppose a stone is dropped from a height of 100 ft. Its position at time t is s(t) =-6r +100. Find…

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

Q: 1. A particle moves along the x-axis according to the equation x-2+3F, where x is in m and is in…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If the brakes on a car give the car a constant negative acceleration of 2k m/s?, where k is a…

A:

Q: A materials scientist is experimenting with a new material with which to make beverage cans. She…

A: From the given plots, the scatterplot shows a perfect negative relationship between the variables.…

Q: An 80-kg skydiver jumps out of an airplane (with zero initial velocity). Assume that k = 12 kg/s…

A: The skydiver's velocity is governed by the differential equation: And the solution to this equation…

Q: a ball is thrown straight upwards from a tower (40 feet high) so that its position, s in feet, at…

A:

Q: 9.Show that the period of motion of an undamped vibration of a mass hanging from a vertical spring…

A:

Q: a weight is bouncing up and down on a spring with height h(feet) after t seconds,  given by h(t)=…

A: We will use derivative to find acceleration equate it to given value

Q: A 0.25-slug mass is attached to a spring and spring is stretched 1.28 ft from its natural length.…

A: Given : A 0.25 mass slug

Q: Two particles have positions at a time t given by the equations x1=t3-t and x2=6t2-t3 find the…

A: If x(t) represents position at time t then velocity = v(t) = dx/dt and acceleration = a(t) = dv/dt =…

Q: Solve the problem. A body of mass m is moving in a straight line with an initial velocity of 2 m/s…

A: Given:-   acceleration⇒6t2-2t+4initial  velocity  of 2m/sec  from origin at  t=0,a=acceleration;…

Q: A cyclist rides down a long straight road at a velocity​ (in m/min) given by v(t)=100−10​t, for…

A:

Q: Because a new employee must learn an assigned task, production will increase with time. Suppose that…

A: To find the number of units completed in t hours by the new employee, integrate the rate of…

Q: dv dt    = −kv2 An object moving through the water has an initial velocity of 40 m/s. Two seconds…

A: As the given differential equation is: dvdt=-kv2 Given conditions are:  t=0 , v=40 mst=2s, v=30 ms…

Q: a car move with an initial velocity of * 50 m/s to the right, determine its position when t=15 s, if…

A: This is a problem related to newton's law of motion. Based on the general formula and concept we…

Q: Suppose that the velocity of a falling body is y = k√s m/sec (k a constant) at the instant the body…

A: The velocity (y) of a falling body is  where k is a constant and s is the function that represents…

Q: Suppose a particle’s position is given by f (t) = −2 / t, where t is measured in seconds and f (t)…

A: Given: ft=-2t

Q: Two particles have positions at time t given by s =4t-t^2 and s=5^2-t^3. Find the velocities v1 and…

A:

Q: A particle is moving such that its position after t hours is s(t) =- -measured in meter. 4t +1 Find…

A:

Q: Car A starts from rest at t = 0 and travels along a straight road with a constant acceleration of 6…

A: Two cars are travelling to each other.

Q: On a different planet, an object is thrown straight upward at an initial speed of 13 m/s and its…

A: We have to integrate the given acceleration function to find the velocity function.  At max. height,…

Q: A ball is thrown upward from a height of 6.5 m at an initial speed of 61 m/sec. Acceleration…

A: here we have .................initial height .................initial velocity ..............gravity

Q: A ball is thrown upward from a height of 0.1 m at an initial speed of 36 m/sec. Acceleration…

A: Given the initial velocity of the ball is u=36 m/s, the acceleration is f=-9.8 m/s2 and was launched…

Q: The velocity function of a particle moving along a horizontal line is given by v(t) = In2 × 23t…

A:

Q: 1. An arrow is shot vertically up into the air with an initial vertical velocity of 60 m/s, and its…

A: Given; Initial velocity=60m/s   h=-5t2+60t.

Q: A particle moves along a straight line from the origin (O) with an initial velocity Va=6ft/sec and…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 – 2t, where 0 <t < 3 (in…

A: Given vt=13-2t, 0≤t≤3,t=3

Q: A particle moves along a straight line and has acceleration given by s"(t) = 5t +3- Its initial…

A: Given,  s''(t)=5t+3, s'(0)=-4, s(0)=7

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: please answer the same way above the former one. a) What is the velocity of the particle at t = 2.8…

A: Answer of (a) as follows :

Q: A ball is thrown upward from a height of 0.9 m at an initial speed of 24 m/sec. Acceleration…

A:

Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

A: A 2‐lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

Q: The rate of growth of a microbe population is given by m'(t) = 22t e ,2t where t is time in days.…

A: We will find the number of microbes in first two days.

Q: A mass-spring system is subjected to a single external force F (t) = sin (t), which acts for 0≤t≤2π…

A: Given mass-spring system is subjected to a single external force F (t) = sin (t), which acts for…

Q: If f(t)=2t+sin(t) describes the length of an oscillating spring in m/s, what is the instantaneous…

A: Solution is written in below steps.

Q: An oil storage tank ruptures at time t =0 and oil leaksfrom the tank at a rate of r(t)  = 100e-0.01t…

A: Given: Oil leaks from the tank at the rate r(t)= 100e-0.01t liters per minute. we have to find how…

Q: Suppose that a furniture removal truck gradually speeds up so that for the first 10s its…

A: We will find out the required values.

Q: |A projectile is launched vertically from the ground at t = 0 and its velocity in flight (in m/s) is…

A:

Q: A mass-spring system is subjected to a single external force F (t) = sin (t), which acts for 0≤t≤2π…

A: Given a mass-spring system is subjected to a single external force F (t) = sin (t), which acts for…

Q: An object with an initial velocity of 40 m/s undergoes an acceleration of a(t) = 12t – 10 m/s“, t…

A:

Q: An object moves along straight like so that after t minutes , its distance from its starting point…

A: Given equation is: xt=10t+5t+1-5 (a) At the end of 4th minutes we get,…

Q: The velocity function of a particle moving along a horizontal line is given by v(t) = ln 2 · 23t,…

A: The Velocity function of the particle moving along a horizontal line is given by v(t)=ln2·23t…

Q: A particle moves along the x-axis so that at any time t ≥ 0 its velocity is given by…

A: Given: v(t)=t2ln(t+2)we know that acceleration of particle is differentiation of velocity of…

Q: 1. A particle moves along the x-axis according to the equation x=2r+3F, where x is in m and is in…

A:

Q: If a ball is thrown vertically upward from the roof of 32 foot building with a velocity of 80…

A: We need to find height, velocity, acceleration.

Q: The height (in centimeters) at time t (in seconds) of a small mass oscillating at the end of a…

A: Height is given by ht=3 sin 2πt→1instantaneous velocity=dhdt⇒Differentiate eqn 1 , w.r.t 't' , we…

Q: A ball is thrown upward from a height of 1.5 m at an initial speed of 45 m/sec. Acceleration…

A: Given that the initial speed=v0=45Initial height=h0=1.5Acceleration=a=-9.8So using the relation…