A. acceleration.

On a Velocity vs Time graph the slope will always be equal to the acceleration. I.e. if the slope is negative, so is the acceleration and vice versa.

5 0

4 years ago

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If the pendulum is taken into the orbiting space station what will happen to the bob? if the pendulum is taken into the orbiting

mezya [45]

Check the attached file for the answer.

3 0

4 years ago

If a ball is thrown vertically upward from the roof of 32 foot building with a velocity of 64 ft/sec, its height after t seconds

stepan [7]

Answer:

a) $s_{max} = 96\,ft$ , b) $v(4.449\,s) = -78.368\,\frac{ft}{s}$

Explanation:

a) The maximum height is obtained with the help of the First and Second Derivative Tests:

First Derivative

$v(t) = 64 - 32\cdot t$

$64 - 32\cdot t = 0$

$t = 2\,s$

Second Derivative

$a(t) = -32$ (absolute maximum)

The maximum height reached by the ball is:

$s (2\,s) = 32 + 64\cdot (2\,s) - 16\cdot (2\,s)^{2}$

$s_{max} = 96\,ft$

b) The time required by the ball to hit the ground is:

$32+64\cdot t - 16\cdot t^{2} = 0$

$-16\cdot (t^{2}-4\cdot t - 2) = 0$

$t^{2}-4\cdot t - 2 = 0$

$(t -4.449)\cdot (t+0.449)\approx 0$

Just one root offers a solution that is physically reasonable:

$t = 4.449\,s$

The velocity of the ball when it hits the ground is:

$v(4.449\,s) = 64 - 32\cdot (4.449\,s)$

$v(4.449\,s) = -78.368\,\frac{ft}{s}$

6 0

3 years ago

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