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Acceleration and Velocity of a Particle

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1. A particle oscillates between the points x = 40 mm and x = 160 mm with an acceleration a = k( 100 - x), where a and x are expressed in mm/ s^2 and mm, respectively, and k is a constant. The velocity of the particle is 18 mm/ s when x = 100 mm and is zero at both x = 40 mm and x = 160 mm. Determine (a) the value of k,( b) the velocity when x = 120 mm.

2. The motion of a particle is defined by the relation x = 1.5t^4 - 30t2 + 5t + 10, where x and t are expressed in meters and seconds, respectively. Determine the position, the velocity, and the acceleration of the particle when t = 4 s.

3. The acceleration of a particle is defined by the relation a = kt^2. (a) Knowing that v =-32 ft/ s when t = 0 and that v =-32 ft/ s when t = 4 s, determine the constant k. ( b) Write the equations of motion, knowing also that x = 0 when t = 4 s.

4. A truck travels 220 m in 10 s while being decelerated at a constant rate of 0.6 m/ s^2. Determine (a) its initial velocity, ( b) its final velocity, ( c) the distance traveled during the first 1.5 s.

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Physics problems: Velocity, Speed, Acceleration

1) Wiley Coyote has missed the elusive roadrunner once again. This time, he leaves the edge of the cliff at 50 m/s horizontal velocity. If the canyon is 100 meters deep, how far from the edge of the cliff does the coyote land?
a) 100 meters
b) 200 meters
c) 225 meters
d) 250 meters
e) 300 meters

2) An artillery shell is fired with an initial velocity of 300 m/s at 55° above the horizontal. It explodes on a mountainside 42 seconds after firing. If x is horizontal and y is vertical, what is the (x, y) coordinates where the shell explodes?
a) x = 7200 m; y = 1700 m
b) x = 5000 m; y = 1300 m
c) x = 3000 m; y = 900 m
d) x = 1500 m; y = 500 m

(Questions 3-4): A ball is thrown horizontally from the top of a building 100 meters high. The ball strikes the ground at a point 65 meters horizontally away from and below the point of release.

3) What is the initial horizontally velocity of the ball?
a) 43 m/s
b) 47 m/s
c) 39 m/s
d) 36 m/s
e) 14 m/s

4) What is the speed of the ball just before it hits the ground?

a) 43 m/s
b) 47 m/s
c) 39 m/s
d) 36 m/s
e) 14 m/s

5) A baseball leaves a bat at an angle of 30 degrees above the horizontal. The ball strikes a fence that is 100 meters horizontally from the barrier at a height of 5.0 meters above the height of the bat when it struck the ball. What was the speed of the ball as it left the bat?

a) 35 m/s
b) 18 m/s
c) 30 m/s
d) 23 m/s
e) 28 m/s

6) A baseball is hit at ground level. The ball is observed to reach its maximum height above ground level 3.0 seconds after being hit. And 2.5 seconds after reaching this maximum height, the ball is observed to barely clear a fence that is 320 ft from where it was hit. How high is the fence? (The acceleration of gravity is -32.2 ft/s2.)

a) 27 feet
b) 52 feet
c) 44 feet
d) 36 feet
e) 16 feet

7) At the lowest point in a vertical dive (radius = 600 m), an airplane has a speed of 300 km/h which is not changing. Determine the magnitude of the acceleration of the pilot at this lowest point.
a) 150 m/s2
b) 21 m/s2
c) 16 m/s2
d) 12 m/s2
e) 8.8 m/s2

8) A particle moves along a circular path having a radius of 2.0 meters. At an instant when the speed of the particle is equal to 3.0 m/s and changing at the rate of 5.0 m/s2, what is the magnitude of the total acceleration of the particle?
a) 9.5 m/s
b) 6.0 m/s2
c) 5.4 m/s2
d) 6.7 m/s2
e) 4.5 m/s2

9) The speed of a particle moving in a circle 3.0 m in diameter increases at a constant rate of 4.0 m/s2. At a particular instant, the magnitude of the total acceleration of the particle is 6.0 m/s2. What is the speed of the particle at this instant?
a) 3.7 m/s2
b) 3.0 m/s2
c) 2.6 m/s2
d) 2.4 m/s2
e) 3.3 m/s2

10) A river has a steady speed of 0.3 m/s. A student swims downstream a distance of 1.2 km and returns to the starting point. If the student swims with respect to the water at a constant speed and the downstream portion of the swim requires 20 minutes, how much time is required for the entire swim?
a) 50 minutes
b) 80 minutes
c) 90 minutes
d) 70 minutes
e) 60 minutes

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