C

9000072901

Level: 
C
The velocity of a moving body in meters per second is given by the function \(v(t) = 3\sqrt{t} + 2t\), where \(t\) is a time measured in seconds. Find the distance traveled by the body in the time interval from \(t = 1\, \mathrm{s}\) to \(t = 9\, \mathrm{s}\).
\(132\, \mathrm{m}\)
\(4\left (4 + \sqrt{2}\right )\mathrm{m}\)
\(10\, \mathrm{m}\)

9000072903

Level: 
C
The force required to deform a spring is proportional to the extension of the spring. The current elongation of the spring is \(2\, \mathrm{cm}\) and the force required to reach this elongation is \(3\, \mathrm{N}\). Evaluate the work required to stretch the spring from the current elongation (i.e. \(2\, \mathrm{cm}\)) by additional \(10\, \mathrm{cm}\).
\(1.05\, \mathrm{J}\)
\(0.75\, \mathrm{J}\)
\(0.18\, \mathrm{J}\)

9000072905

Level: 
C
The \(1000\, \mathrm{kg}\) heavy satellite is transported to the orbit \(150\, \mathrm{km}\) above the ground. Find the mechanical work required for this transport. The mass of the Earth is \(M = 6\cdot 10^{24}\, \mathrm{kg}\), gravitational constant \(\kappa = 6.67\cdot 10^{-11}\, \mathrm{N\, m}^{2}\mathrm{kg}^{-2}\) and Earth radius \(R = 6\: 370\, \mathrm{km}\). Round your result to nearest \(\mathrm{MJ}\).
\(1\: 445\, \mathrm{MJ}\)
\(1\: 471\, \mathrm{MJ}\)
\(1\: 412\, \mathrm{MJ}\)

9000072906

Level: 
C
The reservoir in the form of a box is filled with the water. The vertical side of the box is \(50\, \mathrm{cm}\) height and \(40\, \mathrm{cm}\) long. Find the total force which acts on this side. The mass density of the water is \(1\: 000\, \mathrm{kg\, m}^{-3}\) and the standard acceleration of gravity is \(g = 9.81\, \mathrm{m\, s}^{-2}\).
\(490.5\, \mathrm{N}\)
\(981\, \mathrm{N}\)
\(245.25\, \mathrm{N}\)

9000072907

Level: 
C
A homogeneous cube with the side \(10\, \mathrm{cm}\) is in the water. The bottom side is parallel to the water surface \(10\, \mathrm{cm}\) below the surface. Find the work required to move the cube to the position when the bottom side just touches the surface of the water. The mass density of the cube is \(2\: 000\, \mathrm{kg\, m}^{-3}\), the mass density of the water is \(1\: 000\, \mathrm{kg\, m}^{-3}\) and the standard acceleration of gravity is \(g = 10\, \mathrm{m\, s}^{-2}\).
\(1.5\, \mathrm{J}\)
\(2\, \mathrm{J}\)
\(1\, \mathrm{J}\)

9000072908

Level: 
C
A \(100\, \mathrm{kg}\) heavy anchor is attached to a \(20\, \mathrm{m}\) long rope. One meter of the rope weights \(1\, \mathrm{kg}\). Find the work required to raise the anchor \(20\, \mathrm{m}\) higher. The standard acceleration of gravity is \(9.81\, \mathrm{m\, s}^{-2}\). Neglect the buoyancy (the force from the Archimedes law).
\(21\: 582\, \mathrm{J}\)
\(23\: 544\, \mathrm{J}\)
\(19\: 620\, \mathrm{J}\)

9000072902

Level: 
C
The instantaneous velocity of a moving body is proportional to the square of the time. The velocity at the time \(t = 2\, \mathrm{s}\) is \(v = 6\, \mathrm{m\, s}^{-1}\). What is the distance traveled by the body in the first \(4\) seconds?
\(32\, \mathrm{m}\)
\(48\, \mathrm{m}\)
\(24\, \mathrm{m}\)

9000072904

Level: 
C
The force of the repulsion of two charged particles is \[ F(x) = \frac{c} {x^{2}}, \] where \(x\) is the distance in meters and \(c\) a positive constant. Find the work required to increase the distance between the particles from \(3\, \mathrm{m}\) to \(1\, \mathrm{m}\).
\(\frac{2} {3}c\, \mathrm{J}\)
\(\frac{1} {3}c\, \mathrm{J}\)
\(c\, \mathrm{J}\)