(a) Consider a situation in which the forpe F applied to a particle of mass m is zero. Multiply the scalar form of Eq. (1.2) on page 7 (i.e., a = dv/dt) by dt, and integrate both sides to show that the velocity v (also a scalar) is constant. Then use the scalar form of Eq. (l.l) to show that the (scalar) position r is a linear function of time.
(b) Repeat Part (a) when the force applied to the particle is a nonzero constant, to show that the velocity and position are linear and quadratic functions of time, respectively.
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