Question

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

Answer 1

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

Step-by-step 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