Question

For the one-dimensional motion, described by $x=t-\sin t$

• 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. v (t) lies between 0 and 2.

Answer 1

Answer: (A), (D)

x (t) > 0 for all t > 0
v (t) lies between 0 and 2.

When we draw the graph of t and sint we find that the graph of t lies above sint for all t>0 hence t- sint is always greater than 0 for all t>0.

On differentiating x= t- sint

We get

V= 1 - cost

Which lies between 0 to 2

At t=0, v=0

t=π , v=2

Hence A and D are correct option.