1 The position of a particle as it moves along the x-axis is given by x = 15e-2t
ID: 1628891 • Letter: 1
Question
1 The position of a particle as it moves along the x-axis is given by x = 15e-2t m, where t is in s. What is the acceleration of the particle at t = 1 s?
A. 22 m/s
B. 60 m/s
C. 15 m/s
D. 35 m/s
E. 8.1 m/s
2 The velocity of a particle moving along the x-axis is given for t > 0 by v(x) = (320t - 2.00t^3) 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 -32.0 m/s^2
B -64.0 m/s^2
C Zero
D 128 m/s^2
E 32.0 m/s^2
3 A particle moving along the x-axis has a position given by x = 54t - 2.0t3 m. At the time t = 3.0 s, the speed of the particle is zero. Which statement is correct?
A The particle no longer accelerates after t = 3.0 s.
B The particle can be found at positions x <0 m only when t < 0 s.
C The particle remains at rest after t = 3.0 s.
D All of these answers are correct.
E None of these answers are correct.
5 An object is thrown vertically and has an upward velocity of 18 m/s when it reaches one fourth of its maximum height above its launch point. What is the initial (launch) speed of the object?
A 25 m/s
B 30 m/s
C 21 m/s
D 17 m/s
E 35 m/s
6 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 -275 km/s^2
B -520 km/s^2
C -360 km/s^2
D -500 km/s^2
E-550 km/s^2
9 A car travels north at 30 m/s for one half hour. It then travels south at 40 m/s for 15 minutes. The total distance the car has traveled and its displacement are:
A 90 km; 18 km N.
B 90 km; 36 km N.
C 18 km; 18 km S.
D 36 km; 36 km N.
E 36 km; 36 km S.
10 An automobile manufacturer claims that its product will, starting from rest, travel 0.40 km in 9.0 s. What is the magnitude of the constant acceleration required to do this?
A 6.6 m/s^2
B 4.6 m/s^2
C 8.9 m/s^2
D D 9.9 m/s^2
E 5.6 m/s^2
The position of a particle as it moves along the x-axis is given for t > 0 by x = (t^3 - 3t62 + 6t) m, where t is in s. Where is the particle when it achieves its minimum speed (after t = 0)?
A 8m
B 4m
C 3m
D 7m
E 2m
Explanation / Answer
1.
x = 15 e^-2t
The coefficient of t is -2. Recall that acceleration is the second derivative of displacement. So
velocity = dy/dx = -2 * 15 * e^-2t = -30 e^-2t
acceleration = d2y/dx^2 = -2 * -30 * e^-2t = 60 e^-2t
when t = 1
acceleration = 60 e^-2 = 60 / e^2 = 8.12 m/s^2 (option E)
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