The equation of motion of a particle is s = t3 − 3t, where s is in meters and t is in seconds. (assume t ≥ 0.) (a) find the velocity and acceleration as functions of t. g

Explanation:

The  equation of motion of a particle is :

Where

s is in meters

t is in seconds

The position of a particle is,

The acceleration of a particle is,

Hence, this is the required solution.

Velocity: m/s

Accelaration: m/s²

Explanation:

The velocity is the derivative of the position.

The accelaration is the derivative of the velocity.

Derivative concepts

The derivative of is

The derivative of a subtraction is the subtraction of the derivatives.

The derivative of a constant is 0.

The equation of the position is

m

The equation of the velocity is

Derivative of the position

m/s

The equation of the acceleration is

m/s²

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.