Hello, I want the answer for part c General acceleration. Show your work and exp

Question

Hello, I want the answer for part c

General acceleration. Show your work and explain your reasoning. Two cars both pass the same starting point on a straight track at time t = 0 and their positions relative to that starting point are described by the following equations. x_1(t) = -0.22 t + 12.4 t x_2(t) = 0.14 t^2 + 1.05 m/s t a. Find the instantaneous velocities of these two cars as a function of time. b. Find the instantaneous accelerations of these two cars as a function of time. c. At what time after the two cars cross the do they have the same instantaneous velocity? d. Can these two vehicles ever have the same instantaneous acceleration? Answer and explain. Note that you can answer this without answering part (c).

Explanation / Answer

Given

x1(t) = -0.22t^3 + 12.4 t

x2(t) = 0.14t^2 + 1.05t

a. v1(t) = dx1/dt = -0.66t^2 + 12.4

v2(t) = dx2/dt = 0.28t + 1.05

b. a1(t) = dv1/dt = -1.32t

a2(t) = dv2/dt = 0.28

c. for same vewlocity

v1 = v2

-0.66t^2 + 12.4 = 0.28t + 1.05

0.66t^2 + 0.28t -11.35 = 0

solving for t, t = 3.94 s

d. for same acceleration

a1 = a2

-1.32t = 0.28

t = -0.2121

t < 0 is n ot possible so these vehicles can never have same instantaneous accelerations

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