After moving the mp3 file to the timeline, click on it once, and then hover your mouse pointer on the right edge of the sound clip. You should see a red bracket. You can drag that bracket to the right, and stretch the clip on the timeline. This will allow more of the music to play, and if you stretch it far enough, the whole clip will play.
To know how far to stretch it, right click inside the audio clip in the timeline, and select "open clip." You should see a little audio symbol in the monitor window. Click the play button below it, and the audio will play just as it did in the timeline: too short. When it stops, notice the position of the pointer below the monitor window. Now, stretch the clip in the timeline again, and you should see the pointer in the window move a little to the left. Hit the play button again, and it will play to what it thinks is the end, and stop. Eventually, you'll get the whole clip to play.