The acceleration, in meters per second per second, of a race car is modeled by A(t)=t3−152t2+12t+10, where t is measured in seconds. What is the car's maximum acceleration on the time interval 0≤t≤6 ?

Answer:

  10.237 m/s²

Explanation:

The maximum acceleration will be at one end of the interval, or at a turning point in the interval. The turning points can be found where the derivative of acceleration is zero

  A'(t) = 3t^2 -304t +12

The quadratic formula will tell the zeros of this.

  t = (304±√(304^2 -4(3)(12)))/(2(3)) = (304 -√92272)/6 = (152 -√23068)/3

  t ≈ 0.0394891

Then the maximum acceleration is ...

  A(0.0394891) ≈ 10.23690 . . . . m/s^2

__

Additional comment

The maximum magnitude of acceleration is at t=6, where acceleration is ...

  A(6) = -5174 . . . . m/s^2

This is more than 500 g's in the negative direction, so the race car is not expected to survive that long.

__

The attached graph shows the acceleration curve for positive acceleration. The acceleration continues to decrease to a minimum of -5174 m/s^2 at the right end of the interval [0, 6].

Answer:

AP Statistics teachers from across the country meet annually in Kansas City to score AP Statistics exams. One social event that many teachers participate in is the annual Prediction Fun Run. Prior to the race, the teachers predict how long it will take them to complete the 1.96-mile long course. During the event, they are timed and their actual finishing times are paired with their predicted times. Here is a scatterplot of the results. - Screen shot of the scatter plot and questions below!



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The closeness of the place, and the heat of the climate, added to the number in the ship, which was so crowded that each had scarcely room to turn himself, almost suffocated us. . . .

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Why did James O'Hear Sanders decide to bring a suit
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