Representing Motion Practice Test

A model rocket launches vertically from $y_0=0\ \text{m}$ with initial speed $v_0=18\ \text{m/s}$ upward. After launch, the engine cuts off immediately, so the only force is gravity with $a=-9.8\ \text{m/s}^2$. Air resistance is neglected, and the motion is one-dimensional along the vertical axis. Analyze the motion from $t=0$ until the rocket reaches its peak. Based on the scenario described, determine the maximum height reached by the projectile.

Two carts move on a frictionless track along the $x$ axis toward each other. Cart 1 starts at $x_1=0\ \text{m}$ with constant velocity $+2.0\ \text{m/s}$, and cart 2 starts at $x_2=10\ \text{m}$ with constant velocity $-1.0\ \text{m/s}$. External forces are negligible before the collision, so each cart’s acceleration is zero until impact. Analyze the motion from $t=0$ until the carts collide. Based on the scenario described, calculate the displacement of the object after 5 seconds.