Kinematics of a Particle WWW.CLEAR-MATH.COM
A bicyclist starts from rest and after traveling along a straight path a
distance of 20 m reaches a speed of 30 km/h. Determine his acceleration if it
is constant. Also, how long does it take to reach the speed of 30 km/h?
A car starts from rest and reaches a speed of 80 ft/s after traveling 500 ft along a
straight road. Determine its constant acceleration and the time of travel.
A particle travels along a straight line such that in 2 s it move from an initial position s A = +0.5 m to a position sB =
-1.5 m. Thin in another 4 s it moves from sB to sC = +2.5 m. Determine the particle’s average velocity and average
speed during the 6 s time interval
Course Engineering Mathematics 1 ก่อนสอบ 3 สัปดาห์ เรียน 20 ชม. สอนเนื้อหาได้ 70 % ค่าเรียน 1,500 บาท/คน
เทอม 2 เปิดสอน Engineering Mathematics 2 – 3 , Engineering Mechanics , Calculus 2 , Linear Algebra
Summer เปิดสอน Engineering Mechanics , Engineering Mathematics 1 – 3 , Calculus 1 - 2
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1
Kinematics of a Particle WWW.CLEAR-MATH.COM
From approximately what floor of a building must a car be
dropped from an at rest position so that it reaches a speed of
80.7 ft/s ( 55 mi/h ) when it hits the ground? Each floor is 12 ft
higher than the one below it ( Note: you may want to remember
this when traveling 55 mi/h )
The acceleration of a particle along a straight line is defined by a = ( 2t – 9 ) m/s2 where t is in seconds. At t = 0, s =
1 m and v = 10 m/s. When t = 9 s, determine (a) the particle’s position (b) the total distance traveled (c) the velocity
Course Engineering Mathematics 1 ก่อนสอบ 3 สัปดาห์ เรียน 20 ชม. สอนเนื้อหาได้ 70 % ค่าเรียน 1,500 บาท/คน
เทอม 2 เปิดสอน Engineering Mathematics 2 – 3 , Engineering Mechanics , Calculus 2 , Linear Algebra
Summer เปิดสอน Engineering Mechanics , Engineering Mathematics 1 – 3 , Calculus 1 - 2
086 – 323 – 3270 (พี่ชัย) , 085 – 961 – 7666 (พี่พงษ์)
2
Kinematics of a Particle WWW.CLEAR-MATH.COM
Two particles A and B state from rest at the origin s = 0 and move along a straight line such that a A = ( 6t – 3 ) and
aB = ( 12t2 – 8 ) ft/s2 where t is in seconds. Determine the distance between them when t = 4 s and the total distance
each has traveled in t = 4 s
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3
Kinematics of a Particle WWW.CLEAR-MATH.COM
An airplane starts from rest, travels 5000 ft down a runway and after
uniform acceleration takes off with a speed of 162 mi/h. It then climbs in a
straight line with a uniform acceleration of 3 ft/s2 until it reaches a constant
speed of 220 mi/h. Draw the s – t , v – t and a – t graphs that describe the
motion
The v-s graph for an airplane traveling on a straight runway is shown.
Determine the acceleration of the plane at s = 100 m and s = 150 m. Draw the
a-s graph
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4
Kinematics of a Particle WWW.CLEAR-MATH.COM
The girl always throws the toys at an angle of 30 from point A as shown. Determine the time between throws so
that both toys stride the edges of the pool B and C at the same instant. With what speed must she throw each toy?
The balloon A is ascending at the rate v  12 km/h and is being
carried horizontally by the wind at v  20 km/h. If a ballast bag
is dropped from the balloon at the instant h = 50 m, determine
the time needed for it to strike the ground. Assume that the bag
was released from the balloon with the same velocity as the
balloon. Also, with what speed does the bag strike the ground?
A
W
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5
Kinematics of a Particle WWW.CLEAR-MATH.COM
The man stands 60 ft from the wall and throws a ball at it with a speed 50 ft/s. Determine the angle at which he
should release the ball so that it strikes the wall at the highest point possible. What is this height? The room has a
ceiling height of 20 ft.
Course Engineering Mathematics 1 ก่อนสอบ 3 สัปดาห์ เรียน 20 ชม. สอนเนื้อหาได้ 70 % ค่าเรียน 1,500 บาท/คน
เทอม 2 เปิดสอน Engineering Mathematics 2 – 3 , Engineering Mechanics , Calculus 2 , Linear Algebra
Summer เปิดสอน Engineering Mechanics , Engineering Mathematics 1 – 3 , Calculus 1 - 2
086 – 323 – 3270 (พี่ชัย) , 085 – 961 – 7666 (พี่พงษ์)
6
Kinematics of a Particle WWW.CLEAR-MATH.COM
The ball is throw from the tower with a velocity of 20 ft/s as shown. Determine the x and y coordinates to where the
ball strikes the slope. Also, determine the speed at which the ball hits the ground
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7
Kinematics of a Particle WWW.CLEAR-MATH.COM
The ball is kicked with an initial speed v  8 m/s at an angle   40 with the horizontal. Find the equation of the
path y  f ( x) and then determine the ball’s velocity and the normal and tangential components of its acceleration
when t = 0.2 s

A
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A
8
Kinematics of a Particle WWW.CLEAR-MATH.COM
If a particle’s position is described by the polar coordinates r  4(1  sin t ) m and   (2e ) rad where t is in seconds
and the argument for the sine is in radians, determine the radial and tangential components of the particle’s velocity
and acceleration when t = 2 s
t
A particle moves in the x-y plane such that its position is defined by r  {2ti  4t j } ft where t is in seconds.
Determine the radial and tangential components of the particle’s velocity and acceleration when t = 2 s
2
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9
Kinematics of a Particle WWW.CLEAR-MATH.COM
The slotted link is pinned at O and as a result of the constant angular velocity of 3 rad/s it drives the peg P for a
short distance along the spiral guide r  (0.4 ) m where  is in radians. Determine the radial and transverse
components of the velocity and acceleration of P at the instant    3 rad
Determine the displacement of the block at B it A is pulled down 4 ft
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10
Kinematics of a Particle WWW.CLEAR-MATH.COM
The pulley arrangement shown is designed for hoisting materials. If BC remains fixed while the plunger P is pushed
downward with a speed of 4 ft/s, determine the speed of the load at A
If block A is moving downward at 6 ft/s while block C is moving down at 18 ft/s, determine the relative velocity of
block B with respect to C
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11
Kinematics of a Particle WWW.CLEAR-MATH.COM
If block A of the pulley system is moving downward with a speed of 4 ft/s while block C is moving up at 2 ft/s,
determine the speed of block B
At the instant shown. Cars A and B are traveling at speeds of 30 mi/h and 20 mi/h, respectively. If B is increasing its
speed by 1200 mi/h2 while A maintains a constant speed, determine the velocity and acceleration of B with respect to
A
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12
Kinematics of a Particle WWW.CLEAR-MATH.COM
At the instant shown, the bicyclist at A is traveling at 7 m/s around the curve on the race track while increasing his
speed at 0.5 m/s2 . The bicyclist at B is traveling at 8.5 m/s along the straight-a-way and increasing his speed at 0.7
m/s2 . Determine the relative velocity and relative acceleration off A with respect to B at this instant
Course Engineering Mathematics 1 ก่อนสอบ 3 สัปดาห์ เรียน 20 ชม. สอนเนื้อหาได้ 70 % ค่าเรียน 1,500 บาท/คน
เทอม 2 เปิดสอน Engineering Mathematics 2 – 3 , Engineering Mechanics , Calculus 2 , Linear Algebra
Summer เปิดสอน Engineering Mechanics , Engineering Mathematics 1 – 3 , Calculus 1 - 2
086 – 323 – 3270 (พี่ชัย) , 085 – 961 – 7666 (พี่พงษ์)
13
Kinematics of a Particle WWW.CLEAR-MATH.COM
At a given instant the football player at A throws a football C with a velocity of 20 m/s in the direction shown.
Determine the constant speed at which the player at B must run so that he can catch the football at the same
elevation at which it was thrown. Also calculate the relative velocity and relation acceleration of the football with
respect to B at the instant the catch is made. Player B is 15 m away from A when A starts to throw the throw the
football
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14
Kinematics of a Particle WWW.CLEAR-MATH.COM
Point A oscillates with an acceleration a  144(20  x) where a and x are
expressed in in/s2 and inches, respectively. Knowing that the system starts at
time t = 0 with v = 0 and x = 19 in , determine the position and the velocity
of A when t = 0.2 s
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15
Kinematics of a Particle WWW.CLEAR-MATH.COM
Steep safety ramps are built beside mountain highways to enable vehicles with defective brakes to stop safety. A
truck enters a 250 m ramp at a high speed v and travels 180 m in 6 s at constant deceleration before its speed is
reduced to v 2 . Assuming the same constant deceleration, determine (a) the additional time required for the truck
to stop (b) the additional distance traveled by the truck
0
0
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16
Kinematics of a Particle WWW.CLEAR-MATH.COM
Car A is parked along the northbound lane of a
highway and car B is traveling in the southbound
lane at a constant speed of 96 km/h. At t = 0, A
starts and accelerates at a constant rate a while at
t = 5 s , B begins to slow down with a constant
deceleration of magnitude a 6 . Knowing that
when the cars pass each other x = 90 m and v  v ,
determine (a) the acceleration A (b) when the
vehicles pass each other (c) the distance between the
vehicles at t = 0
A
A
A
B
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17
Kinematics of a Particle WWW.CLEAR-MATH.COM
Block C starts from rest and moves downward with a constant acceleration. Knowing that after 12 s the velocity of
block A is 456 mm/s, determine (a) the acceleration of A, B and C (b) the velocity and the change in position of block
B after 8 s
086 – 323 – 3270 (พี่ชัย) , 085 – 961 – 7666 (พี่พงษ์)
18
Kinematics of a Particle WWW.CLEAR-MATH.COM
Slider block A starts with an initial velocity at t = 0 and a constant acceleration of 9 in/s 2 to the right. Slider block C
starts from rest at t = 0 and moves to the right with constant acceleration. Knowing that at t = 2 s , the velocity of A
and B are 14 in/s to the right and 1 in/s to the left, respectively, determine (a) the acceleration of B and C (b) the
initial velocity of A and B (c) the initial velocity of portion E of the cable
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19
Kinematics of a Particle WWW.CLEAR-MATH.COM
A parachutist is in free fall at a rate of 180 ft/s when he opens his parachute at an altitude of 1900 ft. Following a
rapid and constant deceleration he then descends at a constant rate of 44 ft/s from 1800 ft to 100 ft , where he
maneuvers the parachute into the wind to further slow his descent. Knowing that the parachutist lands with a
negligible downward velocity, determine (a) the time required for the parachutist to land after opening his
parachute (b) the initial deceleration
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20
Kinematics of a Particle WWW.CLEAR-MATH.COM
Car A is traveling at 70 km/h when it enters a 50 km/h speed zone. The driver of car A decelerates at a rate of 5 m/s 2
until reaching a speed of 50 km/h which she then maintains. When car B which was initially 19 m behind car A and
traveling with a constant speed of 72 km/h enters the speed zone ,its driver decelerates at a rate of 6 m/s 2 until
reaching a speed of 48 km/h. Knowing that the driver of car B maintains a speed of 48 km/h, determine (a) the
closest that car B comes to car A (b) the time at which car A is 22 m in front of car B
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21
Kinematics of a Particle WWW.CLEAR-MATH.COM
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22
Kinematics of a Particle WWW.CLEAR-MATH.COM
A baseball pitching machine ‘throws’ baseballs with a horizontal velocity. Knowing that height varies between 788
mm and 1068 mm, determine (a) the range of values of velocity (b) the values of  corresponding to h = 788 mm
and h = 1068 mm
086 – 323 – 3270 (พี่ชัย) , 085 – 961 – 7666 (พี่พงษ์)
23
Kinematics of a Particle WWW.CLEAR-MATH.COM
A golfer hits a golf ball with an initial velocity of 48 m/s at an angle of 25 with the horizontal. Knowing that the
fairway slopes downward at an average angle of 5 , determine the distance d between the golfer and point B where
the ball first lands


In slow pitch softball the underhand pitch must reach a maximum height of between 6 ft and 12 ft above the
ground. A pitch is made with an initial velocity of magnitude 43 ft/s at an angle of 33 with the horizontal.
Determine (a) if the pitch meets the maximum height requirement (b) the height of the ball as it reaches the batter

086 – 323 – 3270 (พี่ชัย) , 085 – 961 – 7666 (พี่พงษ์)
24
Kinematics of a Particle WWW.CLEAR-MATH.COM
Small wheels attached to the ends of rod AB roll along two surfaces. Knowing that at the instant shown the velocity
(b) the
v of wheel B with respect to wheel A is perpendicular to rod AB, determine (a) the relative velocity v
velocity v of wheel B
A
B A
B
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25
Kinematics of a Particle WWW.CLEAR-MATH.COM
Slider block B starts from rest and moves to the right with a constant acceleration of 300 mm/s 2. Determine (a) the
relative acceleration of portion C of the cable with respect to slider block A (b) the velocity of portion C of the cable
after 2 s
086 – 323 – 3270 (พี่ชัย) , 085 – 961 – 7666 (พี่พงษ์)
26
Kinematics of a Particle WWW.CLEAR-MATH.COM
Pin P moves at a constant speed of 8 in/s in a counterclockwise sense along a circular slot which has been milled in
the block A as shown. Knowing that the block moves up the incline at a constant speed of 4.8 in/s, determine the
magnitude and the direction relative to the xy axes of the velocity of pin P when (a)   30 (b)   135

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
27
Kinematics of a Particle WWW.CLEAR-MATH.COM
The rotation of rod OA about O is defined by the relation   0.5e sin 3 t where  and t are expressed in
radians and seconds, respectively. Collar B slides along the rod so that its distance from O is
r  0.2  1.92t  6.72t  6.4t where r and t are expressed in meters and seconds, respectively. When t = 0.5 s,
determine (a) the velocity of the collar (b) the acceleration of the collar (c) the acceleration of the collar relative to
the rod
0.8t
2
3
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28
Kinematics of a Particle WWW.CLEAR-MATH.COM
Pin C is attached to rod BC and slides freely in the slot of rod OA which rotates at the constant rate  . At the
instant when   60 , determine (a) r and  (b) r and  . Express your answers in terms of d and 

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29
Kinematics of a Particle WWW.CLEAR-MATH.COM
Block B starts from rest and moves downward with a constant acceleration. Knowing that after slider block A has
moved 400 mm its velocity is 4 m/s, determine (a) the accelerations of A and B (b) the velocity and the change in
position of B after 2 s
Course Engineering Mathematics 1 ก่อนสอบ 3 สัปดาห์ เรียน 20 ชม. สอนเนื้อหาได้ 70 % ค่าเรียน 1,500 บาท/คน
เทอม 2 เปิดสอน Engineering Mathematics 2 – 3 , Engineering Mechanics , Calculus 2 , Linear Algebra
Summer เปิดสอน Engineering Mechanics , Engineering Mathematics 1 – 3 , Calculus 1 - 2
086 – 323 – 3270 (พี่ชัย) , 085 – 961 – 7666 (พี่พงษ์)
30
Kinematics of a Particle WWW.CLEAR-MATH.COM
An oscillating garden sprinkler which discharges water with an initial velocity of 8 m/s is used to water a vegetable
garden. Determine the distance to the farthest point B that will be watered and the corresponding angle when (a)
the vegetables are just beginning to grow (b) the height h of the corn is 1.8 m
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31
Kinematics of a Particle WWW.CLEAR-MATH.COM
Knowing that at the instant shown block A has a velocity of 8 in/s and an acceleration of 6 in/s2 both directed down
the incline, determine (a) the velocity of block B (b) the acceleration of block B
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32