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

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

area of focus

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.