ES8_ DYNAMICS OF RIGID BODIES
QUIZ 1
Name: __________________________________
Program/Block: ______________
Student I.D. number: _______________
Directions: Answer the following problems with complete solutions and correct units in a
clean piece of paper. Use the last number of your student I.D. number to substitute for
the variable “𝐴” and the fourth number (student I.D.) for the variable “𝑍”.
For example: 2050-00123 (red part is your student number)
A= 3 and Z=2
PROBLEM 1.
The velocity of a point along a horizontal straight line varies according to the equation
𝑣 = 𝐾𝑡 2 – 𝑍𝑡 + 𝐴, where 𝑣 is the magnitude of the velocity in meter per second, and K is
a constant (positive is to the right). The point is 5. 𝐴 meters to the left of the origin when
t = 0 and is 30. 𝐴 meters to the right of the origin when t = 4 sec. Determine
(a) the acceleration of the point when t = 3 sec;
(b) the total distance traveled by the point during the time interval from t = 1 sec to t = 3
sec.
PROBLEM 2
The position of a particle moving along the x axis is given by the equation
1
𝑍
𝑥 = 12𝑡 2 – 3𝑡 3 + cos 𝐴𝜋 𝑡 , where x is in feet and t is in seconds. Positive is to the
right. (a) By the mathematical method determine
(1) the velocity of the particle when t = 1 s and 10 s
(2) the displacement of the particle from t = 1 s to t = 10 s
(3) the total distance traveled from t = 1 s to t = 10 s.
(b) Check (1), (2), and (3) of part (a) with a x-t and v-t diagram.
PROBLEM 3
A car starts from rest and with constant acceleration achieves a velocity of when it travels
a distance of 200 m. Determine the acceleration of the car and the time required.
PROBLEM 4
10
the relation 𝑥 = 𝐴 𝑠𝑖𝑛 2(𝑍)𝑡 + 5𝑐𝑜𝑠2𝑡 + 5 𝑡 defines the motion of a particle , where x and
t are expressed in mm and seconds, respectively. Determine
(a) the position, velocity and acceleration of the particle when 𝑡 = (𝑍 − 𝐴 + 10) 𝑠
(b) the maximum velocity and acceleration of the particle.
PROBLEM 5
A car is traveling at 1𝐴 𝑚/𝑠, when the traffic light 5𝑍 𝑚 ahead turns yellow. Determine the
required constant deceleration of the car and the time needed to stop the car at the light.