Applications of Piecewise Linear Functions and Integrals : Velocity, Time and Acceleration

A car is traveling on a straight road with velocity 55 ft/sec at time t = 0. For 0 ≤ t ≤ 18 seconds, the car's acceleration a(t) , in ft/sec2, is the piecewise linear function defined by the graph above.
(a) Is the velocity of the car increasing at t = 2 seconds? Why or why not?
(b) At what time in the interval 0 ≤ t ≤ 18, other than t = 0 is the velocity of the car 55 ft/sec? Why?
(c) On the time interval 0 ≤ t ≤ 18, what is the car's absolute maximum velocity, in ft/sec, and at what time does it occur? Justify your answer.
(d) At what times in the interval 0 ≤ t ≤ 18, if any, is the car's velocity equal to zero? Justify your answer.

Question: The blades in a blender rotate at a rate of 7290 rpm. When the motor is turned off during operation, the blades slow to rest in 3.67 s. What is the angular acceleration as the blades slow down? The initial rotation is in the positive direction.

The period of a stone swung in a horizontal circle on a 2.00-m radius is 1.00 s.
a. What is its angular velocity in rad/s?
b. What is its linear speed in m/s?
c. What is its radial acceleration in m/s^2.

Question: Bar BDE is attached to two links AB and CD. Knowing that at the instant shown link AB rotates with a constant angular velocity of 3 rad/s clockwise, determine the acceleration (a) of point D, (b) of point E.
Please refer to attachment to see a diagram of this scenario.

Q: "The blades in a blender rotate at a rate of 7290 rpm. When the motor is turned off during operation, the blades slow to rest in 3.67 s. What is the angular acceleration as the blades slow down? The initial rotation is in the positive direction."
The OTA's solution is attached. We both got an answer of 208 rad/s^2.

Please help with the following problem regarding classical mechanics. Please provide step by step calculations.
How far does an object travel and what is its acceleration if its velocity increases at a uniform rate from 9 m/s to 24 m/s in 9 seconds?
Explain the meaning of the slope and area of the velocity vs. time for th

Newton discovered that the falling acceleration of all objects in a vacuum, regardless of their sizes and weights, is the same. A raindrop falls down to earth with the same acceleration as a big metal ball drops from the edge of a building. He came up with the value of 9.8 meters per square second (s2) for the falling accelerati

1. A particle oscillates between the points x = 40 mm and x = 160 mm with an acceleration a = k( 100 - x), where a and x are expressed in mm/ s^2 and mm, respectively, and k is a constant. The velocity of the particle is 18 mm/ s when x = 100 mm and is zero at both x = 40 mm and x = 160 mm. Determine (a) the value of k,( b) the

Given that the acceleration vector is a(t) = (-9cos(-3t)) i + (-9sin(-3t)) j + (-2t) k , the initial velocity is v(0) = i + k , and the initial position vector is r(0) = i+j+k , compute:
A. The velocity vector
B. The position vector

1. A piecewise function is given. Use the function to find the indicated limits, or state that a limit does not exist.
(a) lim is over x gd - f(x), (b) lim is over x gd + f(x), and (c) lim is over xgd f(x)
f(x) = { x^2 - 5 if x < 0 }
{ -2 if x >= 0 } : d = -3
(a) -5 (b) -2 (c) does not exist