14 Un corpo si muove con accelerazione costante lungo l'asse \( s \) di un sistema di riferimento carte- siano. Se il corpo, inizialmente fermo, è partito da \( s_{0}=2,0 \mathrm{~m} \) nell'istante \( t_{0}=0 \mathrm{e} \), trascorsi \( 4,0 \mathrm{~s} \), si trova in \( s_{1}=4,0 \mathrm{~m} \), con quale legge oraria può essere descritto il suo moto? (a) \( s=(2,0 \mathrm{~m})+\left(0,25 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2} \) (b) \( s=(2,0 \mathrm{~m})+\left(0,25 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2} / 2 \) (c) \( s=(2,0 \mathrm{~m} / \mathrm{s})+\left(0,50 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2} \) (d) \( s=(2,0 \mathrm{~m})-\left(0,25 \mathrm{~m} / \mathrm{s}^{2}\right) t \) (e) \( s=(4,0 \mathrm{~m})+\left(0,25 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2} / 2 \)

9.4. (a) Suppose that the unknown resistance \( R_{u} \) in Figure 9.2 is a resistance thermometer whose resistance at \( 100^{\circ} \mathrm{C} \) is \( 500 \Omega \) and whose resistance varies with temperature Chapter 9 at the rate of \( 0.5 \Omega /{ }^{\circ} \mathrm{C} \) for small temperature changes around \( 100^{\circ} \mathrm{C} \). Calculate the sensitivity of the total measurement system for small changes in temperature around \( 100^{\circ} \mathrm{C} \), given the following resistance and voltage values measured at \( 15^{\circ} \mathrm{C} \) by instruments calibrated at \( 15^{\circ} \mathrm{C}: R_{1}=500 \Omega ; R_{2}=R_{3}=5000 \Omega \); \( V_{i}=10 \mathrm{~V} \)

a) Use the kinetic theory of gases to explain the pressure in the gas b) Hence discuss the effect on the pressure of the gas when the gas is heated at constant volume c) On the same axes of a p-V graph, show the change in the pressure of the gas when the gas is heated at constant volume and when the volume of the gas is reducod at constant temperature.

ercice résolu Un corps solide \( (\mathrm{S}) \) de masse \( \mathrm{m}=2,9 \mathrm{~kg} \) glisse avec une vitesse constante \( \mathrm{v}=3,7 \mathrm{~m} / \mathrm{s} \) sur un plan incliné d'un gle \( \theta=35^{\circ} \) par rapport à l'horizontale. Le corps \( (\mathrm{S}) \) est soumis à une force \( \overrightarrow{\mathrm{F}} \) dont la direction est parallèle à la ne de plus grande pente, et de sens opposé à celui du mouvement du corps ( S ) et d'intensité \( \mathrm{F}=1,57 \mathrm{~N} \). On lige les frottements et on prend \( \mathrm{g}=9,8 \mathrm{~N} / \mathrm{kg} \). 1- Faire un schéma de la situation et y représenter les vecteurs forces extérieurs sans respect de l'echelle. 2- Le centre de gravité G du corps solide \( (\mathrm{S}) \) se déplace d'une distance \( \mathrm{AB}=4,7 \mathrm{~m} \). 2.1. Le travail de \( \overrightarrow{\mathrm{F}} \) entre A et B , est-il moteur ou résistant ? Justifier votre réponse. 2.2. Calculer \( \mathrm{W}_{\mathrm{A} \rightarrow \mathrm{B}}(\overrightarrow{\mathrm{F}}) \) et \( \mathrm{W}_{\mathrm{A} \rightarrow \mathrm{B}}(\overrightarrow{\mathrm{P}}) \).

An airplane is supposed to fly with a velocity vector of \( \langle 160,-120\rangle \), but a steady wind has a velocity vector of \( \langle 40,40\rangle \). How much does the wind speed affect the plane's intended velocity vector?

2. एक ही दिशा में चल रहे दो रेल इंजन जिनका वज़न 120 kN व 100 kN हैं, टकराने के पश्चात् एक साथ आगे बढ़ते हैं । टक्कर के पश्चात् समान गति (speed) होगी \( \begin{array}{ll}\text { (1) } 3.8 \mathrm{~m} / \mathrm{s} & \text { (2) } 3.9 \mathrm{~m} / \mathrm{s} \\ \text { (3) } 4.0 \mathrm{~m} / \mathrm{s} & \text { (4) } 4.1 \mathrm{~m} / \mathrm{s}\end{array} \)