Given a particle that has the velocity v(t) = 3 cos(mt) = 3 cos (0.5t) meters, a. find the acceleration at 3 seconds. b. find the displacement at 2 seconds.

a.

b.

Explanation:

Given:

The acceleration of the particle at a time is defined as the rate of change of velocity of the particle at that time.

At time t = 3 seconds,

Note: The arguments of the sine is calculated in unit of radian and not in degree.

The velocity of the particle at some is defined as the rate of change of the position of the particle.

For the time interval of 2 seconds,

The term of the left is the displacement of the particle in time interval of 2 seconds, therefore,

It is the displacement of the particle in 2 seconds.

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.