Suppose a particular plane needs to attain a speed of k feet per second in order to take off. The plane can attain that speed in 30 seconds. Assume acceleration is constant, v(0) = 0, and s(0)=0 when answering the questions below. Use lower case k (a) Find formulas for acceleration, velocity, and position of the plane. Your answers will have k in it. a(t) = v(t) = s(t) = -Select- Select... --Select- V v (b) If the plane accelerates to k feet per second in 30 seconds, how far will it travel in that time? Your answer will have k in it. feet (c) If a runway is 3000 feet long and the plane uses the entire runway to take off, what is the value of k? k=

In the previous Problem Set question, we started looking at the position functions (t), the position of an object at time t. Two important physics concepts are the velocity and the acceleration. If the current position of the object at time is as (t), then the position at time h later is a (t+h). The average velocity (speed) during that additional time his (s(t+h)-s(t)) If we want to analyze the instantaneous velocity at time t, this can be made into a mathematical model by taking the limit as h→0. i.e. the derivative a' (t). Use this function in the model below for the velocity function (). h The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a(t) can be modeled with the derivative of the velocity function, or the second derivative of the position function a(t) = ✔ (t) =" (t). Problem set question: A particle moves according to the position functions (t) = etsin (2). Enclose arguments of functions in parentheses. For example, sin…

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Please answer all of the questions asked. Please show your work.