v=(____i + ____ j)m/s and a=_____m/s^2 A test track for automobiles has a portio
ID: 1823363 • Letter: V
Question
v=(____i + ____ j)m/s and a=_____m/s^2
A test track for automobiles has a portion with a specific profile described by: y = h[1 -cos(x/omega)] where h = 0.3 m and omega = 2 m, and where the argument of the cosine function is understood to be in radians. A car travels in the positive* direction with a constant* component of velocity equal to 81 km/h. Modeling the car as a point moving along the given profile, determine the velocity and acceleration (expressed in m/s and m/S2, respectively) of the car for x = 30 m.Explanation / Answer
Given Vx is constant = 81 * 5/18 = 22.5 m/s Vx = dx/dt Vy = dy/dt y = h - h * cos(x/w) dy/dt = - h * (1/w) * (- sin(x/w)) * dx/dt ---(1) Vy = 0.3 * (1/2) * sin(x/2) * Vx At x = 30 m Vy = 0.3 * 0.5 * sin(30/2) * 22.5 = 2.194 m/s So velocity is V = 22.5 i + 2.194 j m/s For acceleration differentiate eq (1) since Vx is constant ax = 0 d^2y/dt^2 = h * 1/w * 1/w * cos(x/w) * Vx ay = 0.3 * 0.5 * 0.5 * cos(30/2) * 22.5 = -1.28 m/s^2 acceleration is a = 0 i + - 1.28 j
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