What is Xman(t), the position of the man as a function of
time?
Answer symbolically in terms of the variables d, Vman, and
t.
A man is running at speed Uman to catch a bus already at a stop, as shown in (Figure 1). At t=0, when he is a distance d from the door to the bus, the bus starts moving with the positive acceleration abus. Use a coordinate system with x = 0 at the door of the stopped bus.
Answer
Speed of the man = vman.
Hence, distance moved by the man in time t = Speed x Time =
vmant.
At t = 0 s, the position of the man was d unit behind the door
of the stopped bus, i.e., xman ( t = 0 ) = - d.
Therefore, xman ( t ) = - d +
vmant.