Answer
(a) Relative to the flatcar, the motor scooter's velocity is 5.0 m/s to the right.
(b) Relative to the flatcar, the motor scooter's velocity is 16.0 m/s to the left.
(c) Relative to the flatcar, the motor scooter's velocity is 13.0 m/s to the left.
Work Step by Step
Let motion to the right be the positive direction.
Let $F$ be the flatcar.
Let $M$ be the motor scooter.
Let $O$ be the observer.
$v_{M/O} = v_{M/F}+v_{F/O}$
$v_{M/F} = v_{M/O} - v_{F/O}$
(a) $v_{M/F} = v_{M/O} - v_{F/O}$
$v_{M/F} = 18.0~m/s - 13.0~m/s = 5.0~m/s$
Relative to the flatcar, the motor scooter's velocity is 5.0 m/s to the right.
(b) $v_{M/F} = v_{M/O} - v_{F/O}$
$v_{M/F} = -3.0~m/s - 13.0~m/s = -16.0~m/s$
Relative to the flatcar, the motor scooter's velocity is 16.0 m/s to the left.
(c) $v_{M/F} = v_{M/O} - v_{F/O}$
$v_{M/F} = 0 - 13.0~m/s = -13.0~m/s$
Relative to the flatcar, the motor scooter's velocity is 13.0 m/s to the left.
