Linear Motion

A subway train travels a distance $d$ between two stations. The train starts from rest at the first station and comes to a complete stop at the second. The maximum tolerable acceleration magnitude for passengers is $a$. The train stops for a duration $t_{stop}$ at each station.

A car undergoes uniformly accelerated linear motion. The distance between any two consecutive utility poles along the road is 50 m. The car takes 5 s to pass the first interval and 4 s to pass the second interval.

Train A is moving forward at a speed $v_1$. The driver suddenly notices another train B on the same track at a distance $s$ ahead, moving in the same direction at a smaller constant speed $v_2$, where $v_2 < v_1$. The driver of train A immediately applies the brakes, causing a constant deceleration of magnitude $a$.

An object in free fall starts from rest. Its final velocity upon hitting the ground is 10 m/s.

A particle moves in a plane with acceleration given by $\vec{a}(t) = (k_x t)\hat{i} + (k_y t)\hat{j}$, where $k_x$ and $k_y$ are constants. At $t=0$, its initial position is $\vec{r}_0 = r_{0x}\hat{i} + r_{0y}\hat{j}$ and its initial velocity is $\vec{v}_0 = v_{0x}\hat{i} + v_{0y}\hat{j}$.

An object is dropped from rest from the top of a tower. The distance it travels during the final second of its fall is 9/25 of the total height of the tower.

Rocks from a volcano on Jupiter's moon Io are ejected vertically and reach a maximum height of 200 km. The gravitational acceleration on Io is $g_{Io} = 1.80$ m/s², and air resistance is negligible.

An airplane undergoes uniformly decelerated linear motion after landing. In the first $10$ s, it travels a distance of $450$ m. At the end of this period, its velocity is half of its initial landing velocity.

Object A moves with a constant velocity of $v_A = 1$ m/s. 5 seconds after A starts, object B starts from rest from the same location. B undergoes uniformly accelerated linear motion with an acceleration of $a_B = 40$ cm/s² in the same direction as A.

An object is undergoing uniformly accelerated linear motion over a time interval of duration $T$. The initial velocity at the start of the interval is $v_i$ and the final velocity is $v_f$.