In the time interval from 0 s to 15 s, the acceleration of a particle is given by a = (0.1 m/s 3) t for one-dimensional motion. If a particle starts from rest at the origin, calculate its instantaneous velocity at any time during the interval 4 s to 14 s. 1. v (t) = (0.1 m/s 3) t 2 2. v (t) = (0.45 m/s 3) t 2 3. v (t) = (0.05 m/s 3) t 2 4. v (t) = (0.9 m/s 3) t 2

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Physics

Frosty

8 January, 03:57

In the time interval from 0 s to 15 s, the acceleration of a particle is given by a = (0.1 m/s 3) t for one-dimensional motion. If a particle starts from rest at the origin, calculate its instantaneous velocity at any time during the interval 4 s to 14 s. 1. v (t) = (0.1 m/s 3) t 2 2. v (t) = (0.45 m/s 3) t 2 3. v (t) = (0.05 m/s 3) t 2 4. v (t) = (0.9 m/s 3) t 2

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Maxwell Herrera · Answer 1

3. v (t) = (0.05 m/s 3) t 2

Explanation:

Instantaneous acceleration = 0.1 t

dv / dt = 0.1 t

dv = 0.1 t dt

Integrating on both sides

v (t) = (0.1 / 2) t²

=.05 t²