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Kinematics of a Particle
Multiple Choice

1 .       A car is traveling at a speed of 80 ft/s when the brakes are suddenly applied, causing a constant deceleration of 10 ft/s2. Determine the time required to stop the car and the distance traveled before stopping. 



2 .       A particle is moving along a straight line through a fluid medium such that its speed is measured as v = (2t) m/s, where t is in seconds. If it is released from rest at s = 0, determine its positions and acceleration when t = 3 s. 



3 .      

A ball thrown vertically upward from the top of a building with an initial velocity of vA = 35 ft/s. Determine (a) how high above the top of the building the ball will go before it stops at B, (b) the time tAB it takes to reach its maximum height, and (c) the total time tAC needed for it to reach the ground at C from the instant it is released. 



4 .       A small metal particle passes downward through a fluid medium while being subjected to the attraction of a magnetic field such that its position is observed to be s = (15t3 - 3t) mm, where t is measured in seconds. Determine (a) the particle's displacement from t = 2 s to t = 4 s, and (b) the velocity and acceleration of the particle when t = 5 s. 



5 .      

A car, initially at rest, moves along a straight road with constant acceleration such that it attains a velocity of 60 ft/s when s = 150 ft. Then after being subjected to another constant acceleration, it attains a final velocity of 100 ft/s when s = 325 ft. Determine the average velocity and average acceleration of the car for the entire 325-ft displacement. 



6 .      

A car travels up a hill with the speed shown in the graph. Compute the total distance the car moves until it stops at t = 60 s. What is the acceleration at t = 45 s? 



7 .      

A race car starting from rest moves along a straight track with an acceleration as shown in the graph (where for t 10 s, a = 8 m/s2). Determine the time t for the car to reach a speed of 50 m/s. 



8 .      

A two-stage missile is fired vertically from rest with an acceleration as shown in the graph. In 15 s the first stage A burns out and the second stage B ignites. How fast is the rocket moving and how far has it gone at t = 20 s? How fast is the missile moving and how far has it gone at t = 20 s? 



9 .      

From experimental data, the motion of a jet plane while traveling along a runway is defined by the v-t graph shown. Find the position s and the acceleration a when t = 40 s. 



10 .      

The v-s graph for a rocket sled is shown. Determine the acceleration of the sled when s = 100 m and s = 175 m. 



11 .      

The flight path of a jet aircraft as it takes off is defined by the parmetric equations x = 1.25 t2 and y = 0.03 t3, where t is the time after take-off, measured in seconds, and x and y are given in meters. At t = 40 s (just before it starts to level off), determine at this instant (a) the horizontal distance it is from the airport, (b) its altitude, (c) its speed and (d) the magnitude of its acceleration. 



12 .      

For a short time the missile moves along the parabolic path y = (18 - 2x2) km. If motion along the ground is measured as x = (4t - 3) km, where t is in seconds, determine the magnitudes of the missile's velocity and acceleration when t = 1 s. 



13 .      

The motorcyclist attempts to jump over a series of cars and trucks and lands smoothly on the other ramp, i.e., such that his velocity is tangent to the ramp at B. Determine the launch speed vA necessary to make the jump. 



14 .      

The boy throws a snowball such that it strikes the wall of the building at the maximum height of its trajectory. If it takes t = 1.5 s to travel from A to B, determine the velocity vA at which it was thrown, the angle of release , and the height h



15 .      

A ball is thrown downward on the 30° inclined plane so that when it rebounds perpendicular to the incline it has a velocity of vA = 40 ft/s. Determine the distance R where it strikes the plane at B



16 .       A boat is traveling along a circular path having a radius of 20 m. Determine the magnitude of the boat's acceleration if at a given instant the boat's speed is v = 5 m/s and the rate of increase in speed is v = 2 m/s2



17 .       A train travels along a horizontal circular curve that has a radius of 200 m. If the speed of the train is uniformly increased from 30 km/h to 45 km/h in 5 s, determine the magnitude of the acceleration at the instant the speed of the train is 40 km/h. 



18 .      

A sled is traveling down along a curve which can be approximated by the parabola y = x2. When point B on the runner is coincident with point A on the curve (xA = 2m, yA = 1 m), the speed if B is measured as vB = 8 m/s and the increase in speed is dvB/dt = 4 m/s2. Determine the magnitude of the acceleration of point B at this instant. 



19 .      

When the motorcyclist is at A he increases his speed along the vertical circular parth at the rate of v = (0.3t)ft/s2, where t is in seconds. If he starts from rest when he is at A, determine his velocity and acceleration when he reaches B



20 .      

A package is dropped from the plane which is flying with a constant horizontal velocity of vA = 150 ft/s at a height h = 1500 ft. Determine the radius of curvature of the path of the package just after it is released from plane at A. 



21 .      

A package is dropped from the plane which is flying with a constant horizontal velocity of vA = 150 ft/s at a height h = 1500 ft. Determine the radius of curvature of the path of the package just before it is released from plane at A. 



22 .      

A car is traveling along the circular curve of radius r = 300 ft. At the instant shown, its angular rate of rotation is = 0.4 rad / s, which is increasing at the rate of = 0.2 rad / s2. Determine the magnitude of the acceleration of the car at this instant. 



23 .      

A car is traveling along the circular curve of radius r = 300 ft. At the instant shown, its angular rate of rotation is = 0.4 rad / s, which is increasing at the rate of = 0.2 rad / s2. Determine the magnitude of the velocity of the car at this instant. 



24 .      

For a short time the position of a roller-coaster car along its path is defined by the equations r = 25 m, = (0.3t) rad, and z = (-8 cos) m, where t is measured in seconds, Determine the magnitudes of the car's velocity and acceleration when t = 4s. 



25 .      

The slotted link is pinned at O, and as a result of rotation it drives the peg P along the horizontal guide. Compute the magnitude of the velocity and acceleration of P along the horizontal guide. Compute the magnitudes of the velocity and acceleration of P as a function of if = (3t) rad, where t is measured in seconds. 



26 .      

The cylindrical cam C is held fixed while the rod AB and bearings E and F rotate about the vertical axis of the cam at a constant rate of = 4 rad/s. If the rod is free to slide through the bearings, determine the magnitudes of the velocity and acceleration of the guide D on the rod as a function of . The guide follows the groove in the cam, and the groove is defined by the equations r = 0.25 ft and z = (0.25 cos ) ft. 



27 .      

If the end of the cable at A is pulled down with a speed of 2 m/s, determine the speed at which block B arises. 



28 .      

The mine car is being pulled up to the inclined plane using the motor M and the rope-and-pulley arragement shown. Determine the speed vp at which a point P on the cable must be traveling toward the motor to move the the car up the plane with a constant speed of v = 5 m/s. 



29 .      

The block B is suspended from a cable that is attached to the block at E, wraps around three pulleys, and is tied to the back of a truck. If the truck starts from rest when xD is zero, and moves forward with a constant acceleration of aD = 2 m/s2, determine the speed of the block at the instant xD = 3 m. 



30 .       A fly traveling horizontally at a constant speed enters the open window of a train and leaves through the opposite window 3 m away 0.75 s later. If the fly travels perpendicular to the train's motion as seen from an observer on the ground, and the train is traveling at 3 m/s, determine the speed of the fly as observed by a passenger on the train. 



31 .      

As the instant shown, cars A and B are traveling at speeds of 20 mi/h and 45 mi/h, respectively. If B is acceleration at 1600 mi/h2 while A maintains a constant speed, determine the magnitudes of the velocity and acceleration of A with respect to B



32 .      

A passenger in the automobile B observes the motion of the train car . At the instant shown, the train has a speed of 18 m/s and is reducing its speed at a rate of 1.5 m/s2. The automobile is accelerating at 2 m/s2 and has a speed of 25 m/s. Determine the velocity and acceleration of A with respect to B. The train is moving along a curve of radius = 300 m. 



33 .      

If the hoist H is moving upward at 6 ft/s, determine the speed at which the motor M must draw in the supporting cable. 



34 .      

The pilot of flighter plane F is following 1.5 km behind the pilot of bomber B. Both planes are originally traveling at 120 m/s. In an effort to pass the bomber, the pilot in F gives his plane a constant acceleration of 12 m/s2. Determine the speed at which the pilot in the bomber sees the pilot of the fighter plane pass at the start of the passing operation the bomber is decelerating at 3 m/s2. Neglect the effect of any turning. 



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