Answer to Question #242056 in Molecular Physics | Thermodynamics for Milly

Question

A body starts from an origin with initial velocity and moves along the x-axis. Derive an expression for the final velocity v of the distance covered.
B). A train passes a station A at 40kmh-¹and maintain this speed for 10km and is then uniformly retarded stopping at the same time as the first train.
I. On the same diagram sketch the velocity time graph for the two trains.
ii. Find the greatest speed of the second train on the journey.  

Answer 1

a) $s=\frac{v^2-v_0^2}{2a}\to v=\sqrt{2as+v_0^2}$ if $a=0$ then $v=v_0$

b) So, we have

A train passes a station A at 40 km/h and maintains its speed for 10 km and is then uniformly retarded, stopping at B which is 12 km from A. A second train starts from A at the instant the first train passes and being accelerated some part of the journey and uniformly retarded for the rest, stops at B at the same times as the first train.

$10=40\cdot t_1\to t_1=0.25\ (h)$

$12-10=\frac{1}{2}\cdot40\cdot\Delta t\to \Delta t=0.1\ (h)$

$Total \ \ time =0.1+0.25=0.35\ (h)$

$12=\frac{1}{2}\cdot v_2\cdot0.35\to v_2=68.57\ (km/h)$ . Answer