b) Find the point's acceleration at the specified time. s"(2) = ft/sec2 %3D

Q: Suppose an object is moving along a line such that the acceleration after t seconds is 6t -8t…

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Q: A4) The position of a hummingbird flying along a straight line in t seconds is given by S(t) = 6t³ –…

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Q: When d is in feet, t in second , find the velocity at t= 2 of the motion s = t^2 +3t

A: s=t2+3tVelocity of the particle isdsdt=2t+3On putting the value oft=2

Q: A particle travels along a straight line with a velocity v=(12 - 3t®)m/s, where t is in seconds.…

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Q: Given: v(t) = (t + 1)i + (3t)j Position at t = 1 is (4,9) Find the speed at t = 3. speed = √?

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Q: b) A racecar travels on the flat road and its motion is monitored. i) If the car is accelerating at…

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Q: a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t,…

A: Given, a projectile launched at t = 0 second that follows a path x=30t, y=-5t^2+80t where x…

Q: ight, in metres, of an object that has fallen from a height of 180 m is given sition function s(t) =…

A: We will find the required.

Q: Explain why the integral ex*dx is convergent.

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Q: You are videotaping a race from a stand 132 ft. from the track, following a car that is moving at…

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Q: At time t seconds, the center of a bobbing cork is 2sin(2t) centimeters above or below water level.…

A: ft=2sin2t Now velocity is the derivative of position with respect to time. So differentiating…

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.