The motion of a particle is defined by the relation x = t3 – 12t2 +36t +32, where x and t are expressed in feet and seconds, respectively. determine the time, position, and acceleration of the particle when v = 0 ft/s.

1) Time: 2 s, 6 s

The position of the particle is given by:

where t is the time in seconds and x is the position in feet.

The velocity of the particle can be found by differentiating the position:

and it is expressed in ft/s.

In order to find the time at which the velocity is v=0 ft/s, we substitute v=0 into the previous equation:

So the two solutions are

t = 2 s

t = 6 s

2) Position: x = 64 ft and x = 32 ft

The position at which the velocity of the particle is v = 0 can be found by susbtituting t = 2 and t = 6 into the equation for the position.

For t = 2 s, we have

For t = 6 s, we have

So the two positions are

x = 64 ft

x = 32 ft

3) Acceleration: and

The acceleration of the particle can be found by differentiating the velocity. We find:

And substituting t = 2 and t = 6, we find the acceleration when the velocity of the particle is zero:

So the two accelerations are

layer a is the exosphere and layer b is the thermosphere.   is the answer i think but i hope this .

weather forecasts are done by collecting data about the current state of the atmosphere mainly the temperature, humidity and wind and using meteorology, to determine the atmosphere that evolves over time. the h and l mean the high and low pressure. the red strip is a warm front. the blue strip is a cold front. the blue and red strip is a stationary front. the purple strip is a occluded front.

explanation: