Suppose a rock falls from rest from a height of 100 meters and the only force acting on it is gravity. Find an equation for the velocity v(t) as a function of time, measured in meters per second. Hint What is the initial velocity of the rock?

Q: The position of a moving object is s(t)=t^3-2t^2-8t+5 feet away from 0 at t minutes. How long, in…

A:

Q: Show that if acceleration is constant, then the change in velocity isproportional to the length of…

A: Show that if acceleration is constant, then the change in velocity is proportional to the length of…

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: An object with an initial velocity of – 85 m/s undergoes an acceleration of a(t) = 6t + 18 m/s“, t…

A: Given, v=-85 at t=0. a=6t+18

Q: Ex. 1. A shot of mass m, is fired from a gun of mass m2 with velocity v relative to the gun; show…

A:

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

A:

Q: Let r(t) =. Describe the motion of a particle following this path. What happens to its speed as time…

A:

Q: A particle moves vertically (in inches) along the yaxis according to the position equation s(t) = -…

A:

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

A:

Q: d. Without doing any computations, what do you expect to be the instantaneous velocity of the ball…

A: Since   s(t) = 64 - 16(t - 1)² As we can see that at t = 1 , the above quadratic equation has its…

Q: A large water tower holds 3 million gallons of water, which has a mass of about 11 million…

A: As there are multipart to the question, we’ll solve the first three parts. If you want further parts…

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

A:

Q: If the position of an object is s(t) = 16 + 10.5t – 4.9t meters from zero in t seconds, then what is…

A:

Q: The temperature at a point on a metal surface is T (x, y. z) = 0.05x² – 0.01y³ – z in degrees…

A:

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: Assume that an object has a constant acceleration of 10 m / s ^ 2  . Initially, the object is…

A:

Q: The repulsive force f between the north poles of two magnets is inversely proportional to the square…

A: Given that the repulsive force(f) is inverly ptoportional to square of distanceF α 1d2F=kd2First of…

Q: An object with a mass of 10.00kg is launched from the ground with an initial upward velocity of…

A:

Q: Find the displacement of a particle moving in a straight line with velocity v(t) = 4t − 3 m/s over…

A:

Q: 6) A weight oscillates in a vertical motion according to the position function y(f) = -5 cos t.…

A: Acceleration for position function yt=-5cost is d2ydt2. Calculate double derivative d2ydt2 and…

Q: A particle moves along a coordinate line in such a way that its velocity at any time t is given by…

A: We have, a particle moves along a co-ordinate line in such a way that its velocity at any time t is…

Q: A parachutist of mass m falls from rest in the Earth's gravitational field and is subjected to mg…

A:

Q: 1.)Supposed that a mass weighing 10 lbs. stretches a spring 2 inches. If the mass is displaced…

A:

Q: A pendulum consists of a 3.5 kg stone swinging on a 4.1 m string of negligible mass. The stone has a…

A:

Q: An object with a mass of 10.00kg is launched from the ground with an initial upward velocity of…

A:

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: In Winter an aluminum beam was brought from the outside cold into a machine shop where the…

A:

Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

A:

Q: 3- If a ball v leased to fall at t=0 sec according to the law S =;gt where g is the acceleration due…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: ) Suppose that the acceleration function of a particle moving along a coordinate line is a(t) = t –…

A: a)Givena(t) = t - 3Now average acceleration is given by ∫aba(t)dtb-aHere a=0 and…

Q: A spring has a natural length of 10 feet, and when an 64lb weight is attached, the spring measures…

A: Consider the provided question,

Q: 2. A plane travels 560 km from Los Angeles to San Francisco in 1 hour (h). If the plane's velocity…

A:

Q: A sailboat is running along a straight course with thewind providing a constant forward force of 50…

A: Given: A sailboat is running along a straight course with thewind providing a constant forward force…

Q: An electron moves with a constant horizontal velocity of 3.0 x 100 m/s and no initial vertical…

A:

Q: A projectile is fired straight up from a platform 10ft above the ground, with an initial velocity of…

A: Topic:- application of integration

Q: A 3 kg mass is attached to a spring with stiffness k = 48N / m. The mass moves 1/2 m to the left of…

A: The equation can be given as; y" + (k/m)y =0,   The mass moves 1/2 m to the left of the equilibrium…

Q: A runner starts from rest and accelerates at 2 m/s?. Assuming constant acceleration for the entire…

A: Given that a runner starts from rest and accelerates at  2 m/s2. And the acceleration is constant…

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: A comet passing by a star, with initial velocity (30, 60), experiences a force which causes it to…

A:

Q: Find the velocity and acceleration of a body moving according to the following equation S-ts.1 when…

A:

Q: An object with a mass of 10.00kg is launched from the ground with an initial upward velocity of…

A: Given that, An object with a mass of 10.00kg is launched from the ground with an initial upward…

Q: If the velocity is given by : (-t^2 i + 2t^2 j+ t^2 k) then the normal component of the acceleration…

A:

Q: A particle is thrown vertically upwards in the air. The distance it covers in time t is given by…

A: We will be using the fact that rate of change in distance is called velocity. v(t)=dsdt

Q: Determine the velocity of the particle at t = 7.

A:

Q: A sky diver weighing 192 lb (including equipment) falls vertically downward from a very high…

A: Given:

Q: A particle moves on the 0x axis with acceleration proportional to velocity. Assuming that v(0) = 3,…

A:

Q: A spring oscillates with a frequency of 8 cycles per second. Its initial displacement is 3…

A:

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: If s(t) represents the position of an object at time t which quantity represents the acceleration of…

A: To determine which of the given expression represents the acceleration of the object at t=4  if the…

Q: body mass 4 kg falls(at rest) from a medium whose resisting force is numerically equal to 0.003v,…

A: Topic:- Basic maths