Problem 1. A ball is thrown straight up into the air from a height of 5 feet and at an initial speed of 20 feet/second. Let s(t) denote the vertical position of the ball (measured in feet), v(t) denote the velocity of the ball (measured in feet/second), and a(t) denote the acceleration of the ball (measured in feet/second?). From physics, we know that s'(t) = v(t) and v'(t) = a(t). The careful reader will notice you have also been given s(0) and v(0) already for this particular situation. you are told that the ball's acceleration is given by a(t) = -16, find an equation for the po- sition of the ball (that is, find s(t)). (Hint: you are finding a particular solution of a differential equation with two initial conditions, provided above). If

Q: (1) A particle has an initial displacement of s= 30 metres when t = 0. The velocity of the particle…

A: We know that the velocity is defined as the rate of change of the position of the object with…

Q: Suppose an object is moving along a line such that the acceleration after t seconds is 6t -8t…

A:

Q: Use implicit differentiation to find dv/dL.

A: We will use concepts of differentiation in this.

Q: 1.)  Let s(t)= tlnt-t be the displacement of a particle (in feet) from the origin after t seconds.…

A: Velocity and acceleration from displacement function

Q: 1 mdv dt 10 dv dt = mg-bv; v(0) = v = (10) (9.81)-50 v

A: mdvdt=mg-bv, v0=v10dvdt=109.81-50v, v0=0

Q: A train moves along a track at velocity v. Bionica walks down the aisleof the train with velocity u…

A:

Q: 1. A model for the position x (t) of an Olympic jump skier says that the acceleration a(t) = x" is…

A: As per as our guidelines i am supposed to answer only three parts of this question Please repost the…

Q: An object of mass 5 kg is given an initial downward velocity of 40 m/sec and then allowed to fall…

A: Given:Mass Initial downward velocity Acceleration due to gravity Force due to air resistance Drag…

Q: Let y(t) be the height (in meters) after time t (in seconds) of a rover that is landing on some…

A:

Q: Let y(t) be the height (in meters) after time t (in seconds) of a rover that is landing on some…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: