1 The position of a particle as it moves along the x -axis is given by x = 15 e

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

(2) ans

Given that

velocity V=320t-2t^3

now we find the acceleration

acceleration a=dv/dt=d/dt(320t-2t^3)

=320-6t^2

=320-6*(0)

=320 m/s^2

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