# Instantaneous Velocity - Page 5

Questions

- What's the value of the two#?# ? I don't understand what's the question is asking actually and have no idea on what method to use to calculate. :(
- A light on the ground is 30 feet away from a building. A 4 foot man is walking from the light to the building at a rate of 3 feet per second and is casting a shadow on the building. At what rate is his shadow shrinking when he is 5 feet from the building?
- How do I antidifferentiate from acceleration to velocity?
- During surgery, a patient's circulatory system requires at least 50 mg of an anesthetic. The amount of anesthetic present #t# hours after 80 mg of anesthetic are administered is #A(t) = 80(0.727)^t#?
- Determine the position functionif the ac- celeration function is a(t) = 3 sin t+1 , the initial velocity is v(0)=0 and the initial position s(0)=4?
- The displacement s, measured in meters for a body moving from a fixed point, P, at a time of t seconds is given by #s(t) = 10-5te^-(t/10)#. Determine the expression for the velocity v(t)?
- A particle moves along the x-axis so that at time t its position is given by s(t) = (t + 3)(t −1)^3, t > 0. For what values of t is the velocity of the particle decreasing?
- Find initial position via intergration???
- A particle moves in x-y plane so that at any time t its coordinates are x = t^2 - 1, and y = t^4 - 2t^3. What is its acceleration vector at t = 1?
- The volume of a balloon which is being blown increases at the rate of (60-3t^2)cm^3s^-1, where t is the time in seconds. If the initial volume of the balloon is zero, it's volume after 3 sec is?
- (i) Show that the value of **k** is 0.1. (ii) Find an expression for the displacement of the particle from the origin in terms of t?
- Integrals Question With approximately what velocity does a diver enter the water after diving from a 30-m platform? (Use g=9.8m/sec). Thank you!!!
- A particle travels along a number line. Its position at time t is given by s(t)=t^2-3t+2? (cont. below)
- A particle moves in a straight line so that at time t its displacement from a fixed origin is x and its velocity is v. If its acceleration is 4 + x and v = 1 when x = 0, what is v when x = 1?
- A ladder 5m long is standing vertically, flat against a vertical wall, while its lower end in on the horizontal floor. ... Find the speed at which the upper end is moving down the wall 4 seconds after the lower end has left the wall ?
- A 3m ladder has a bent rung 2m from its base. How fast is the distance the bent rung is from the wall changing when the base of the ladder is 1.7m from the wall and the top of the ladder is sliding down the wall 1m/s?
- A kit is 100 ft high. There are 260 ft of string out and it is being let out at a rate of 5 ft/sec. If this results in the kite being carried along horizontally, what is the horizontal speed of the kite?
- For an object whose velocity in ft/sec is given by v(t) = 2sin(t), what is its distance, in feet, travelled on the interval t = 1 to t = 5?
- The position of an object any this given by s(t)=2t^2 -8t+10 a. Determine the velocity of the object? b. Is the object moving to the right or left at t=1? c.is the object right or left at t=4?
- Given the acceleration as (3t^2+2)i+6e^(-2t) j+10cos 5tk, find the magnitude of velocity at t=0?