Question

For the one-dimensional motion, described by $\mathrm { X } = \mathrm { t } - \sin \mathrm { t }$

• A. x(t) > 0 for all t > 0
• B. v(t) > 0 for all t > 0
• C. a(t) > 0 for all t > 0
• D. All of these

Answer 1

Answer: (A)

x(t) > 0 for all t > 0

Answer 2

x = t – sin t

$v = \frac { d x } { d t } = 1 - \cos t$

$\mathrm { a } = \frac { \mathrm { dv } } { \mathrm { dt } } = \sin \mathrm { t }$

$\therefore$x (t) > 0 for all values of t > 0 and v (t) can be zero for one value of t. a (t) can zero for one value of t.