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.

This question will strengthen your concepts of linear motion. A graph showing variation of velocity of a car moving along a straight line is given. You are required to find acceleration of the car at different moments of timeand its displacement.

The coordinates of a bird flying in the XY-plane are given by x(t)=at and y(t) = 3.0 m - Bt^2, where a = 2.4m/s and B = 1.2m/s2.
Calculate the velocity andacceleration vectors of the bird as functions of time.

This graph is for understanding the concepts of variable velocity, uniform velocity, uniform acceleration, negative acceleration, displacement and average velocity of a body moving along a straight line.
Answer the following questions:
a. What is the velocity of the car at 2, 8, 16 and 20 s?
b. What is the acceleration of t

A model rocket is fired vertically upward from rest. It's acceleration for the first three seconds is a(t)=60t at which time the fuel is exhausted and it becomes a free falling body. After 17 seconds, the rocket's parachute opens and the velocity slows linearly to -18 ft/sec in 5 seconds. The rocket then floats to the ground

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.

2. A particle moves along a straight line so that its acceleration at time t seconds is (t + 1)2 cm/sec2. The particle's position at time t = 0 is at the origin, and its initial velocity is 1 cm/sec. What is the position of the particle, in cm. at time t seconds?
A.((t+1)4/12)+(2/3)t-1/12 B.((t+1)4/12)+(2/3)t+1/12 C.((t+1

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.