**P. 4760.** The speed of a car travelling on a highway is \(\displaystyle v_0\). At a certain instant the speed of the car is started to vary uniformly, and from that instant the first 84 m is covered in 3 s, and the next 84 m is covered in 4 s.

Determine the initial speed of the car \(\displaystyle v_0\), and its acceleration \(\displaystyle a\).

(4 points)

**P. 4761.** The acceleration of a strange car is inversely proportional to its speed in the speed interval of \(\displaystyle (v_1,v_2)\), so \(\displaystyle a=A/v\) (\(\displaystyle A\) is a positive constant).

\(\displaystyle a)\) How long does it take for the car to speed up from the speed \(\displaystyle v_1\) to the speed \(\displaystyle v_2\)?

\(\displaystyle b)\) What is the power of the car during this motion?

(4 points)

**P. 4762.** A piece of iron is attached to the bottom of a wooden cylinder of cross section \(\displaystyle A_0\), so the wooden cylinder is floating in a sample of liquid of density \(\displaystyle \varrho_1\), which liquid is in a beaker of cross-section \(\displaystyle A_1\). The beaker is also floating in some liquid of density \(\displaystyle \varrho_2\), in another bigger beaker of cross section \(\displaystyle A_2>A_1\). This beaker is also floating in some liquid of density \(\displaystyle \varrho_3\) in another even wider beaker of cross-section \(\displaystyle A_3>A_2\), and so on...\(\displaystyle \,\). Altogether there are \(\displaystyle n\) beakers on the table. The symmetry axes of all beakers and the wooden cylinder are vertical.

Then the wooden cylinder is pushed down by a vertical force of \(\displaystyle F\). (Neither the wooden cylinder nor any of the beakers touch the other beaker below them.)

\(\displaystyle a)\) By what amount did the height of immersed part of the wooden cylinder in the first liquid increase?

\(\displaystyle b)\) By what amount did the level of the liquid in the first liquid increase?

\(\displaystyle c)\) By what amount did the level of the liquid in the \(\displaystyle i\)-th beaker increased?

(5 points)

**P. 4765.** A coil of inductance 250 mH, and of resistance 0.3 \(\displaystyle \Omega\) is connected to a battery of constant terminal voltage. How much time elapses until the current through the coil reaches

\(\displaystyle a)\) 50% of the stationary final value;

\(\displaystyle b)\) 75% of the stationary final value?

(4 points)