Kinematics

One-Dimensional Motion

A car moves along a straight road with a speed of 200 km/h. When this car passes through another car, initially at rest at a gas station, it begins to move with constant acceleration \( 4.5\ \text{m/s}^{2} \) until it reaches the speed of 200 km/h. Calculate
a) What is the time elapsed until the car leaving the gas station reaches the speed of 200 km/h?
b) How far are they from each other when their speeds are equal.

Free Fall

On the Moon a stone is released at rest from a height of 20 meters, it falls under the action of the lunar free-fall acceleration until reaching the ground with a speed v. Determine how high the stone should be dropped on Earth so that it hits the ground at the same speed v. Free-fall acceleration on Earth \( g_{\text{T}}=9.8\;\text{m/s}^{2} \), free-fall acceleration on the Moon \( g_{\text{L}}=1.6\;\text{m/s}^{2} \).