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- Question : 1RP - Initially, the car travels along a straight road with a speed of 35 m/s. If the brakes are applied and the speed of the car is reduced to 10 mls in 15 s, determine the constant deceleration of the car.
- Question : 2RP - A ball is thrown vertically upward with a speed of 15 m/s. Determine the time of flight when it returns to its original position
- Question : 3RP - A particle travels along a straight line with a velocity of v = (4( - 3(2) mis, where ( is in seconds. Determine the position of the particle when t = 4 s. s = 0 when ( = O.
- Question : 4RP - A particle travels along a straight line with a speed v = (0.5(3 - S() mis, where ( is in seconds. Determine the acceleration of the particle when ( = 2 s.
- Question : 5RP - The posItIOn of the particle is given by s = (2(2 - St + 6) m, where ( is in seconds. Determine the time when the velocity of the particle is zero, and the total distance traveled by the particle when ( = 3 s.
- Question : 6RP - A particle travels along a straight line with an acceleration of a = ( 1 0 - 0.2s) m/s2, where s is measured in meters. Determine the velocity of the particle when s = 10 m if v = 5 mls at s = O
- Question : 7RP - A particle moves along a straight line such that its acceleration is a = (4(2 - 2) m/s2, where ( is in seconds. When t = 0, the particle is located 2 m to the left of the origin, and when ( = 2 s, it is 20 m to the left of the origin. Determine the position of the particle when ( = 4 s.
- Question : 8RP - A particle travels along a straight line with a velocity of v = (20 - 0.05s2) mis, where s is in meters. Determine the acceleration of the particle at s = 15 m.
- Question : 9RP - A car starts from rest and with constant acceleration achieves a velocity of 15 m/s when it travels a distance of 200 m. Determine the acceleration of the car and the time required.
- Question : 10RP - A train starts from rest at a station and travels with a constant acceleration of 1 m/s2. Determine the velocity of the train when ( = 3 0 s and the distance traveled during this time
- Question : 11RP - An elevator descends from rest with an acceleration of 5 ft/s2 until it achieves a velocity of 15 ft/s. Determine the time required and the distance traveled.
- Question : 12RP - A car is traveling at 15 mis, when the traffic light 50 m ahead turns yellow. Determine the required constant deceleration of the car and the time needed to stop the car at the light.
- Question : 13RP - A particle is moving along a straight line with the acceleration a = (12( - 3(1/2) ft/s2, where ( is in seconds. Determine the velocity and the position of the particle as a function of time. When ( = 0, v = 0 and S = 15 ft.'
- Question : 14RP - A ball is released from the bottom of an elevator which is traveling upward with a velocity of 6 ft/s. If the ball strikes the bottom of the elevator shaft in 3 s, 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
- Question : 15RP - A car has an initial speed of 25 m/s and a constant deceleration of 3 m/s2. Determine the velocity of the car when ( = 4 S. What is the displacement of the car during the 4-s time interval? How much time is needed to stop the car?
- Question : 16RP - If a particle has an initial velocity of va = 12 ft/s to the right, at Sa = 0, determine its position when ( = 10 s, if a = 2 ft/S2 to the left.
- Question : 17RP - The acceleration of a particle traveling along a straight line is a = kjv, where k is a constant. If S = 0, v = Va when ( = 0, determine the velocity of the particle as a function of time t.
- Question : 18RP - Car A starts from rest at ( = 0 and travels along a straight road with a constant acceleration of 6 ft/S2 until it reaches a speed of 80 ft/s. Afterwards it maintains this speed. Also, when t = 0, car B located 6000 ft down the road is traveling towards A at a constant speed of 60 ft/s. Determine the distance traveled by car A when they pass each other.
- Question : 19RP - A particle travels along a straight line with a velocity v = (12 - 3(2) mis, where t is in seconds. When ( = 1 s, the particle is located 10 m to the left of the origin. Determine the acceleration when t = 4 s, the displacement from t = 0 to t = 10 s, and the distance the particle travels during this time period.
- Question : 20RP - A sphere is fired downwards into a medium with an initial speed of 27 m/s. If it experiences a deceleration of a = ( - 6t) m/s2, where ( is in seconds, determine the distance traveled before it stops.
- Question : 21RP - A particle travels along a straight line such that in 2 s it moves from an initial position SA = +0.5 m to a position SB = - 1 .5 m. Then 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
- Question : 22RP - A particle travels along a straight-line path such that in 4 s it moves from an initial position SA = -8 m to a position SB = +3 m. Then in another 5 s it moves from SB to Sc = -6 m. Determine the particle's average velocity and average speed during the 9-s time interval
- Question : 23RP - Tests reveal that a normal driver takes about 0.75 s before he or she can react to a situation to avoid a collision. It takes about 3 s for a driver having 0.1 % alcohol in his system to do the same. If such drivers are traveling on a straight road at 30 mph (44 ft/s) and their cars can decelerate at 2 ft/S2, determine the shortest stopping distance d for each from the moment they see the pedestrians. Moral: If you must drink, please don't drive !
- Question : 24RP - As a train accelerates uniformly it passes successive kilometer marks while traveling at velocities of 2 m/s and then 10 m/s. Determine the train's velocity when it passes the next kilometer mark and the time it takes to travel the 2-km distance
- Question : 25RP - A ball is thrown with an upward velocity of 5 m/s from the top of a 10-m high building. One second later another ball is thrown vertically from the ground with a velocity of 10 m/s. Determine the height from the ground where the two balls pass each other
- Question : 26RP - A car starts from rest and moves with a constant acceleration of 1 .5 m/s2 until it achieves a velocity of 25 m/s. It then travels with constant velocity for 60 seconds. Determine the average speed and the total distance traveled.
- Question : 27RP - 19. A car is to be hoisted by elevator to the fourth floor of a parking garage, which is 48 ft above the ground. If the elevator can accelerate at 0.6 ft/s2, decelerate at 0.3 ft/S2, and reach a maximum speed of 8 ft/s, determine the shortest time to make the lift, starting from rest and ending at rest.
- Question : 28RP - A particle is moving along a straight line such that its speed is defined as v = ( -4s2) mis, where s is in meters. If s = 2 m when t = 0, determine the velocity and acceleration as functions of time.
- Question : 29RP - Two particles A and B start from rest at the origin
- Question : 30RP - A particle moving along a straight line is subjected to a deceleration a = ( -2v3) m/s2, where v is in m/s. If it has a velocity v = 8 m/s and a position s = 1 0 m when t = 0, determine its velocity and position when t = 4 s.
- Question : 31RP - A particle is moving along a straight line such that its acceleration is defined as a = (-2v) m/s2, where v is in meters per second. If v = 20 m/s when s = 0 and t = 0, determine the particle's position, velocity, and acceleration as functions of time.
- Question : 32RP - A particle starts from rest and travels along a straight line with an acceleration a = (30 - 0.2v) ft/S2, where v is in ft/s. Determine the time when the velocity of the particle is v = 30 ft/s.
- Question : 33RP - When a particle is projected vertically upwards with an initial velocity of vo, it experiences an acceleration a = - (g + kv2) , where g is the acceleration due to gravity, k is a constant and v is the velocity of the particle. Determine the maximum height reached by the particle.
- Question : 34RP - The acceleration of a particle traveling along a straight line is a = (0.02el) m/s2, where t is in seconds. If v = 0, s = 0 when t = 0, determine the velocity and acceleration of the particle at s = 4 m .
- Question : 35RP - A particle moves along a straight line with an acceleration of a = 5/(3s1/3 + s5/2) m/s2, where s is in meters. Determine the particle's velocity when s = 2 m, if it starts from rest when s = 1 m. Use Simpson's rule to evaluate the integral.
- Question : 36RP - If the effects of atmospheric resistance are accounted for, a falling body has an acceleration defined by the equation a = 9.81[1 - v2(1O-4)] m/s2, where v is in m/s and the positive direction is downward. If the body is released from rest at a very high altitude, determine (a) the velocity when t = 5 s, and (b) the body's terminal or maximum attainable velocity (as t ?? (0).
- Question : 37RP - The position of a particle along a straight line is given by s = ( 1 .5t3 - 13.5t2 + 22.5t) ft, where t is in seconds. Determine the position of the particle when t = 6 s and the total distance it travels during the 6-s time interval. Hint: Plot the path to determine the total distance traveled.
- Question : 38RP - The velocity of a particle traveling along a straight line is v = Vo - ks, where k is constant. If s = 0 when t = 0, determine the position and acceleration of the particle as a function of time.
- Question : 39RP - 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 = 1 m 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.
- Question : 40RP - B all A is thrown vertically upward from the top of a 30-m-high-building with an initial velocity of 5 m/s. At the same instant another ball B is thrown upward from the ground with an initial velocity of 20 m/s. Determine the height from the ground and the time at which they pass.
- Question : 41RP - A motorcycle starts from rest at t = 0 and travels along a straight road with a constant acceleration of 6 ft/S2 until it reaches a speed of 50 ft/s. Afterwards it maintains this speed. Also, when t = 0, a car located 6000 ft down the road is traveling toward the motorcycle at a constant speed of 30 ft/s. Determine the time and the distance traveled by the motorcycle when they pass each other
- Question : 42RP - A particle moves along a straight line with a velocity v = (200s) mm/s, where s is in millimeters. Determine the acceleration of the particle at s = 2000 mm. How long does the particle take to reach this position if s = 500 mm when t = O?
- Question : 43RP - A particle has an initial speed of 27 m/s. If it experiences a deceleration of a = ( -6t) m/s2, where t is in seconds, determine its velocity, after it has traveled 10 m. How much time does this take?
- Question : 44RP - The acceleration of a particle traveling along a straight line is a = (8 - 2s) m/s2, where s is in meters. If v = 0 at s = 0, determine the velocity of the particle at s = 2 m, and the position of the particle when the velocity is maximum.
- Question : 45RP - Ball A is thrown vertically upwards with a velocity of Vo. B all B is thrown upwards from the same point with the same velocity t seconds later. Determine the elapsed time t < 2vo/g from the instant ball A is thrown to when the balls pass each other, and find the velocity of each ball at this instant.
- Question : 46RP - As a body is projected to a high altitude above the earth's surface, the variation of the acceleration of gravity with respect to altitude y must be taken into account. Neglecting air resistance, this acceleration is determined from the formula a = -go[R2/(R + yf] , where go is the constant gravitational acceleration at sea level, R is the radius of the earth, and the positive direction is measured upward. If go = 9.81 m/s2 and R = 6356 km, determine the minimum initial velocity (escape velocity) at which a projectile should be shot vertically from the earth's surface so that it does not fall back to the earth. Hint: This requires that v = O as y ----> 00
- Question : 47RP - Accounting for the vanatlOn o f gravitational acceleration a with respect to altitude y (see Prob. 12-38), derive an equation that relates the velocity of a freely falling particle to its altitude. Assume that the particle is released from rest at an altitude Yo from the earth's surface. With what velocity does the particle strike the earth if it is released from rest at an altitude Yo = 500 km? Use the numerical data in Prob. 12-38.
- Question : 48RP - When a particle falls through the air, its initial acceleration a = g diminishes until it is zero, and thereafter it falls at a constant or terminal velocity vf. If this variation of the acceleration can be expressed as a = (g/v2f) (v2f - v2), determine the time needed for the velocity to become v = vf/2. Initially the particle falls from rest.
- Question : 49RP - A particle is moving along a straight line such that its position from a fixed point is s = (12 - 15t2 + 5t3) m, where t is in seconds. Determine the total distance traveled by the particle from t = 1 s to t = 3 s. Also, find the average speed of the particle during this time interval.
- Question : 50RP - The particle travels along a straight track such that its position is described by the s-( graph. Construct the v-( graph for the same time interval

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