A motorcyclist moves in the opposite direction of an oriented frame of reference, the magnitude of its speed is 40 m/s,
and initially, his position is −150 m. Find:
a) The displacement as a function of time;
b) In what time it passes the origin.
- speed of the motorcyclist: |v| = 40 m/s;
- position at initial time: S0 = −150 m.
We choose a reference frame with the positive direction oriented to the right.
a) We want to find a function of the type
the initial position is given in the problem, S0
= −150 m, as the motorcyclist moves against
the orientation of the reference frame, its speed is negative (v<0), we have v
= −40 m/s. The function
for displacement will be
b) When the motorcyclist passes through the origin we have S
= 0, substituting this value in the expression
found in item (a), we have
as there is no negative time, this means that the motorcyclist
does not pass through the origin of the reference frame
(he starts the motion to the left of the origin and moves to the left away from the origin).