10. The distance travelled by a free falling object varies directly to the square of the time taken. Given that an object dropped a distance of 19.6 m after 2 seconds, find the distance dropped after 5 seconds.

Ejemplo 2 Encontremos la velocidad de una bala de 0.02 kg que adquiere una energia cinética de 400 J. \( \begin{array}{lll}\text { Datos: } \\ m=0.02 \mathrm{~kg} & E_{k}=\frac{1}{2} m v^{2} \\ E_{k}=4001 & \frac{2 E_{k}}{m}=v^{2} & \begin{array}{l}\text { Despejamos la velocidad dejándola e } \\ \text { uno de los lados de la ecuación. }\end{array}\end{array} \)

A 10 kg crate is placed on a rough horizontal surface \( \mu_{\mathrm{k}}=0.4 \) and connected with 12 kg hanging mass via a string that passes over a massless and frictionless pully as shown in the figure beside. Thé mass ( kg ) that must be added to the crate so that the crate moves with constant velocity is:

(5) Ahmed pulls his little sister Noha in a sled on an iey surface (assume no friction), with a force of 60.0 N at an angle of \( 37.0^{\circ} \) upward from the horizontal. If he pulls her 12.0 m , what is the work done by Ahmed? \( \begin{array}{llll}\text { A) } 185 \mathrm{~J} & \text { B) } 433 \mathrm{~J} & \text { C) } 575 \mathrm{~J} & \text { (D) } 720 \mathrm{~J}\end{array} \)

A mass m is traveling at an initial speed \( v_{i}=25.0 \mathrm{~m} / \mathrm{s} \). it is brought to rest in a di ff 62.5 m by a force of 15.0 N . The mass is:

A \( 20-\mathrm{m} \) long steel wire (cross-section \( 1 \mathrm{~cm}^{2} \), Young's modulus \( 2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2} \) ), is subjected to a load of \( 25,000 \mathrm{~N} \). How much will the wire stretch under the load? \( \begin{array}{lllll}\text { A) } 0.25 & \text { B) } & 2.5 \mathrm{~cm} & \text { C) } 12.5 \mathrm{~cm} & \text { D) } 25 \mathrm{~cm}\end{array} \) \( \begin{array}{llll} & \text { B) } 1.25 \mathrm{~cm}\end{array} \)