Asnowboarder starts from rest at the top of a double black diamond hill. as he rides down the slope, gps coordinates are used to determine his displacement as a function of time, x = 0.5t3 + t2 + 2t, where x and t are expressed in feet and seconds, respectively. determine the position, velocity, and acceleration of the boarder expressed when t = 12 seconds. (round the final answer to one decimal place.)

Explanation:

Howdy!

To solve this question we need to know that the velocity v and acceleration a are the first and second derivatives of the position x respect to the time t.

Let's calculate these derivatives:

If we use the following formula:

--- (1)

we get that:

--- (2)

Now the acceleration:

Therefore:

--- (3)

To determine the position, velocity and acceleration at t=12 we must evaluate these functions at t=12:

Evaluating these equations we obtain the required values:

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260 miles per hour

explanation:

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s