Spring 2015-2016 Prof. Dr. Ahmed Abdel-Naby, Dr. Mohamad Kanaan, Dr. Amr Ibrahim & Dr. Amine Moughlbay
Beirut Arab University
Department of Mechanical Engineering
MCHE 213 Assignment #1
[1] A car starts from rest with constant acceleration achieves a velocity 15m/s when it travels a
distance of 200m. Determine its acceleration and the time required.
Ans: aC  0.5625m / s 2 ; t  26.7s
[2] A baseball is thrown downward from a 50-ft tower with an initial speed of 18 ft/s. Determine the
speed at which it hits the ground and the time of travel. Use g  32.2 ft / s 2 .
Ans: v  59.53 ft / s; t  1.29s
[3] A particle travels along a straight line such that in 2s it moves from an initial position S A=+0.5m
to position SB = -1.5m. Then in another 4s it moves from SB to SC = +2.5m. Determine the
particle’s average velocity and average speed during the 6-s time interval.
[4] Traveling with an initial speed of 70 km/h, a car accelerates at 6000 km/h2 along a straight road.
How long will it take to reach a speed of 120 km/h? Also, through what distance does the car
travel during this time?
[5] The acceleration of a particle as it moves along a straight line is given by a  (2t  1) m/s2 where t
is in seconds. If s = 1m and v = 2 m/s when t = 0, determine the particle’s velocity and position
when t = 6 s. Also, determine the total distance the particle travels during this time period.
Ans: v  32m / s; s  67m; d  66m
[6] A particle travels along a straight line with a velocity v = (12 - 3t2) m/s, where t in seconds.
When t = 1s, the particle is located 10m to the left of the origin. Determine the acceleration when
t = 4s, the displacement from t = 0 to t = 10s, and the distance the particle travels during this time
period.
Ans: s  880m; sT  912m
[7] A ball is released from the bottom of an elevator which is traveling upward with a velocity of
6ft/s. if the ball strikes the bottom of the elevator shaft in 3s, determine the height of the elevator
from the bottom of the shaft at the instant the ball is released. Also, find the velocity of the ball
when it strikes the bottom of the shaft.
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Spring 2015-2016 Prof. Dr. Ahmed Abdel-Naby, Dr. Mohamad Kanaan, Dr. Amr Ibrahim & Dr. Amine Moughlbay
Ans: h  127 ft ; v  90.6 ft / s 
[8] The sports car travels along a straight road such that its position is described by the graph.
Construct the v-t and a-t graphs for time interval 0 t 10s.
[9] The v-s graph describing the motion of a motorcycle is shown in figure. Construct the a-s graph
of the motion and determine the time needed for the motorcycle to reach the position s = 400 ft.
Ans: t  12s
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Spring 2015-2016 Prof. Dr. Ahmed Abdel-Naby, Dr. Mohamad Kanaan, Dr. Amr Ibrahim & Dr. Amine Moughlbay
[10] A car starts from and has an acceleration described by the graph. Construct the v-t graph for the
time interval 0 t t’, where t’ is the time for the car to come to rest.
[11] Determine the maximum height on the wall to which the firefighter can project water from the
hose, if θ = 45° and the speed of the water at the nozzle is vC  48 ft / s .
Ans: h  20.4 ft
[12] The ball is kicked from point A with the initial velocity vA = 10m/s. Determine the range R, and
the speed when the ball strikes the ground.
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Spring 2015-2016 Prof. Dr. Ahmed Abdel-Naby, Dr. Mohamad Kanaan, Dr. Amr Ibrahim & Dr. Amine Moughlbay
[13] The snowmobile is travelling at 10 m/s when it leaves the embankment at A. Calculate R and
determine the speed at which it strikes the ground at B.
Ans: R  19m; vB  19.47m / s
[14] The man stands 60 ft from the wall and throws a ball at it with a speed v0  50 ft / s . Determine
the angle θ 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.
Ans:   38.4; h  14.8 ft
[15] A particle is travelling along the parabolic path y  0.25x 2 as shown below.
If x  2t 2 m, where t is in seconds,
(a) Determine the magnitude of the particle’s velocity and acceleration when t = 2 s.
(b) Calculate the tangential component of the particle’s acceleration at the same instant.
Ans: (a) v  32.98m / s; a  48.17m / s 2 (b) at  47.54m / s 2
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Spring 2015-2016 Prof. Dr. Ahmed Abdel-Naby, Dr. Mohamad Kanaan, Dr. Amr Ibrahim & Dr. Amine Moughlbay
[16] A toboggan is travelling down along a curve which can be approximate d by the parabola:
y = 0.01x2. Determine the magnitude of its acceleration when it reaches point A, where its
speed is vA = 10 m/s, and it is increasing at the rate of (at) A = 3 m/s2.
[17] If the motorcycle has a deceleration of at = - (0.001s) m/s2 and its position A is 25 m/s,
determine the magnitude of its acceleration when it passes point B.
[18] When the car reaches point A, it has a speed of 25 m/s. If the brakes are applied, its speed is
reduces by at = (0.001s-1) m/s. Determine the magnitude of acceleration of the car just before it
reaches point C.
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Spring 2015-2016 Prof. Dr. Ahmed Abdel-Naby, Dr. Mohamad Kanaan, Dr. Amr Ibrahim & Dr. Amine Moughlbay
[19] The velocities of skiers A and B ( v A  10m / s and vB  14m / s ) are as shown. Determine the
velocity of A with respect to B
Ans: v A / B  5.05m / s;  55.8
[20] Car B is traveling along the curved road with a speed of 15 m/s while decreasing its speed at 2
m/s2. At this same instant car C is traveling along the straight road with a speed of 30 m/s
while decelerating at 3 m/s2. Determine the velocity and acceleration of car B relative to car C.
Ans: vB / C  18.6m / s and  v  66.2 ; aB / C  0.959m / s 2 and  a  8.57
[21] Two planes A and B are travelling with the constant velocities shown. Determine the magnitude
and direction of the velocity of plane B relative to plane A
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Spring 2015-2016 Prof. Dr. Ahmed Abdel-Naby, Dr. Mohamad Kanaan, Dr. Amr Ibrahim & Dr. Amine Moughlbay
[22] Determine the speed of cylinder A, if the rope is drawn towards the motor M at a constant rate of
10 m/s.
Ans: v A  3.33m / s 
[23] If block A is moving downward at 6 ft/s while block C is moving down at 18 ft/s, determine the
speed of block B.
Ans: vB  12 ft / s 
[24] Determine the displacement of the block B if A is pulled down 4 ft.
Ans: sB  2 ft 
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Spring 2015-2016 Prof. Dr. Ahmed Abdel-Naby, Dr. Mohamad Kanaan, Dr. Amr Ibrahim & Dr. Amine Moughlbay
[25] determine the speed of the elevator if each motor draws in the cable with a constant speed of 5
m/s.
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