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- The accompanying graph plots the best quadratic fit, a(t) = − 0.70t^2 + 1.44t + 10.44, to the data from the preceding table. Compute the average value of a(t) to estimate the average acceleration between t=0 and t=5.Given the function s(t)= -16t2 + 128t, what is the average velocity at time interval [1,2]? Then make a conjecture about the value of the instantaneous velocity at t=1.then what is y at x=1??
- The following data was obtained when the stopping distance d of a car on a wet roadwas measured as a function of the speed v when the brakes were applied: X 2 3 5 6 7 8 F(x) 3 18 38 289 300 450 Table 11- Use Natural Cubic Spline interpolation with the data presented in table 1If the area of the triangle included between the axes and any tangent to the curve x^ n * y = a ^ n is constant, then find the value of n.Integrate the following function both analytically and numerically. For the numerical evaluationsuse (a) a single application of the trapezoidal rule, (b) Simpson’s 1y3 rule, (c) Simpson’s 3y8 rule,
- Derive the following expressions with respect to time (t). For both x and y. y ((vy(t), vy(t)). to find an expression that gives us the value of the velocity x1= L1cosθ1 +L1cosθ2 y1= L1sinθ1+L1sinθ2For the position function, s(t)=-16t2+103t, complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = 1. time interval [1,2] [1,1.5] [1,1.1] [1,1.01] [1,1.001] average velocity
