A particle confined to motion along the x axis moves with constant acceleration from x = 2.0 m to x = 8.0 m during a 2.5-s time interval. The velocity of the particle at x = 8.0 m is 2.8 m/s. What is the acceleration during this time interval?
a. 0.48 m/s2
b. 0.32 m/s2
c. 0.64 m/s2
d. 0.80 m/s2
e. 0.57 m/s2
[Ques. 2] A particle moving along the x axis has a position given by x = (24t 2.0t3) m, where t is measured in s. What is the magnitude of the acceleration of the particle at the instant when its velocity is zero?
a. 24 m/s2
b. zero
c. 12 m/s2
d. 48 m/s2
e. 36 m/s2
[Ques. 3] The position of a particle as it moves along the x axis is given by x = 15e2t m, where t is in s. What is the acceleration of the particle at t = 1.0 s?
a. 22 m/s
b. 60 m/s
c. 8.1 m/s
d. 15 m/s
e. 35 m/s
[Ques. 4] The position of a particle as it moves along the x axis is given for t > 0 by x = (t3 3t2 + 6t) m, where t is in s. Where is the particle when it achieves its minimum speed (after t = 0)?
a. 3 m
b. 4 m
c. 8 m
d. 2 m
e. 7 m
[Ques. 5] The velocity of a particle moving along the x axis is given for t > 0 by vx = (32.0t 2.00t3) m/s, where t is in s. What is the acceleration of the particle when (after t = 0) it achieves its maximum displacement in the positive x direction?
a. 64.0 m/s2
b. zero
c. 128 m/s2
d. 32.0 m/s2
e. 32.0 m/s2
[Ques. 6] The position of a particle moving along the x axis is given by x = 6.0t2 1.0t3, where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction?
a. 24 m
b. 12 m
c. 32 m
d. 16 m
e. 2.0 m
[Ques. 7] A bullet is fired through a board, 14.0 cm thick, with its line of motion perpendicular to the face of the board. If it enters with a speed of 450 m/s and emerges with a speed of 220 m/s, what is the bullet's acceleration as it passes through the board?
a. 500 km/s2
b. 550 km/s2
c. 360 km/s2
d. 520 km/s2
e. 275 km/s2
[Ques. 8] The position of a particle moving along the x axis is given by x = (21 + 22t 6.0t2) m, where t is in s. What is the average velocity during the time interval t = 1.0 s to t = 3.0 s?
a. 6.0 m/s
b. 4.0 m/s
c. 2.0 m/s
d. 8.0 m/s
e. 8.0 m/s
[Ques. 9] The basic function of a carburetor of an automobile is to atomize the gasoline and mix it with air to promote rapid combustion. As an example, assume that 30 cm3 of gasoline is atomized into N spherical droplets, each with a radius of 2.0 105 m. What is the total surface area of these N spherical droplets?
[Ques. 10] What is the mass of air in a room that measures 5.0 m 8.0 m 3.0 m? (The density of air is 1/800 that of water).
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