An object is thrown in the air with vertical velocity of 20 ft/s and horizontal velocity of 15 ft/s. The object’s height can be described by the equation y (t) = −16t2+20t  while the object moves horizontally with constant velocity 15 ft/s. Write parametric equations for the object’s position, and then eliminate time to write height as a function of horizontal position. How did you arrive at your conclusion(s) for this problem? Use the graphical equation editor if necessary to express your answer.

An object moves in the x-y plane with a constant acceleration of 2i +3j meters per second squared. The object starts at the origin with some initial velocity. After four seconds (4 seconds) the velocity of the object is 2i + 8j meters per second. Determine the object’s initial velocity. Leave answer in i-j notation. Determine the position of the object at time, t = 4 seconds. Leave answer in i-j notation.   Thank you for your help.

A circular racetrack has a radius of 500 m. What is the displacement of a bicyclist when she travels around the track from the north side to the south side? When she makes one complete circle around the track? Explain.

Problem 5: A vehicle accelerates down an on ramp and eventually reaches highway speed. The position of the vehicle is described by the following equation: x(t) = AP(1+B) %3D Part (a) Write an expression for the vehicle's instantaneous velocity as a function of time. Expression : v(t) = Select from the variables below to write your expression. Note that all variables may not be required. а, В, л, ө, А, В, d, g, h,j, k, m, Р, S, t Part (b) What is the initial velocity of the vehicle? Numeric : A numeric value is expected and not an expression. Vo = Part (c) What is the vehicle's velocity after accelerating for 10 seconds? The equation's parameters are as follows. A = 34 m/s B = 21 s Numeric : A numeric value is expected and not an expression. v(t) = Part (d) After accelerating, the velocity of the vehicle will begin to level off at highway speed. Write an expression for the vehicle's velocity after it has been accelerating for a long time. Expression : v(t=00) = Select from the variables…

Problem 3: Continue drawing the motion diagram below of an object in steady (constant velocity) traveling in the horizontal axis every 1 second, indicating the velocity vectors along the motion. t = 0 sec V t = 1 sec Problem 4: Continue drawing the motion diagram below of an object in a free-fall motion every 1 second, indicating the velocity vectors along the motion. v = 0 m/s V t = 0 sec t = 1 sec

The kinematic equations can describe phenomena other than motion through space and time. Suppose x represents a person's bank account balance. The units of x would be dollars ($) and velocity v would give the rate at which the balance changes (in units of, for example, $/month). Acceleration would give the rate at which v changes. Suppose a person begins with one hundred dollars in the bank. Initial money management leads to no net change in the account balance so that  v0 = 0.  Unfortunately, management worsens over time so that  a = −3.82 ✕ 102 $/month2.  Assuming a is constant, find the amount of time in months until the bank account is empty.    ?months