For the one-dimensional motion, described by x = t - sint, the following statements are given.
(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
Choose the correct option:
1. (a, c)
2. (b, c)
3. (a, d)
4. (b, d)
(3) Hint: The first derivative of x gives velocity and the first derivative of velocity gives acceleration.
Step 1: Find the velocity and acceleration.
Given,
Step 2: Put the different values of t to find the correct answer.
As acceleration a > 0 for all t > 0
Hence, x(t) > 0 for all t > 0
Velocity v= 1 - cos t
When cos t = 1, velocity v = 0
Hence, v lies between 0 and 2.
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