1. A student is on a stationary train - Scottish Highers Physics - Question 1 - 2017

To find the distance travelled by the train while it accelerates, we can use the equation of motion:

$s = ut + \frac{1}{2}at^2$

where:

• $u = 0\,m/s$ (initial velocity)
• $a = 0.32\,m/s^2$ (acceleration)
• $t = 25\,s$ (time)

Substituting the values: $s = (0)(25) + \frac{1}{2}(0.32)(25^2)$ $s = 0 + \frac{1}{2}(0.32)(625)$ $s = 100\,m$

Thus, the distance travelled by the train is 100 meters.

To find the speed of the train, we can use the Doppler effect formula:

$f_s = f_r \frac{v + v_r}{v + v_s}$

Where:

• $f_s = 270\,Hz$ (source frequency)
• $f_r = 290\,Hz$ (received frequency)
• $v = 340\,m/s$ (speed of sound)
• $v_s$ = speed of the train (unknown)
• $v_r = 0\,m/s$ (observer at rest)

Rearranging gives: $f_r(v + v_s) = f_s(v + v_r)$ $290(v) + 290(v_s) = 270(v)$

Simplifying:

As the train approaches the bridge, the sound waves are compressed due to the train moving towards the observer, resulting in a higher frequency being heard (the Doppler effect). However, once the train passes the bridge, the sound waves are stretched as the train moves away, causing a decrease in the frequency heard by the observer. This change illustrates the inverse relationship between frequency and the relative motion of the source and the observer.