Many years ago they decided to have a parade in Manhattan to awaken people as to the holiness of Shabbos and to encourage Jews to close their stores. So they got 6,000 children together to walk a little over a mile and the Rabbis and Roshei Yeshiva would travel in front of the children in cars. When Rav Moshe Feinstein arrived at the place where the parade started he began to walk by foot. They told him that the Rabbis and Roshei Yeshiva are supposed to ride in cars.
Answered Reb Moshe ztz"l: "Vas? De kinder vellen gain tzu fus und ich vet zitzn in a car? Oib zei gayen tzu fus, gai ich tzu fus" [What? The children go by foot and I am going to sit in a car? If the children go by foot - I am also going to go by foot!"].
When Reb Moshe started to walk all of the Rabbis followed suit.
[Kol Hatorah Nissan 5763]