The acceleration of a race car as a function of time is a(t)= kt,where a is measured in meters per second squared,t is measured in seconds and k is a constant.If its velocity at t = 0 is 2 m/s,and it is 26 m/s at t = 2 s,what is the value of the constant,k? A)12 m/s³ B)12 m/s² C)24 m/s³ D)24 m/s² E)13 m/s³

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Quizplus · Accepted Answer

The velocity function is the integral of the acceleration function. Integrating a(t) = kt gives v(t) = (k/2)t^2 + C. Using the initial condition v(0) = 2, we find C = 2. Using v(2) = 26, we solve (k/2)(2)^2 + 2 = 26, which gives k = 12 m/s³.

The Acceleration of a Race Car as a Function of Time