A particle moves with acceleration a(t) = -4*v(t). If initial velocity v(0) = 16 m/s, what is v(t)?
Answer and explanation
Correct answer: B. v(t) = 16 * e^(-4t)
- Step 1: dv/dt = -4v => (1/v) dv = -4 dt => ln|v| = -4t + C. Step 2. v(t) = v(0)e^(-4t) = 16e^(-4t). *Answer: v(t) = 16 e^(-4t). Why not the others:** The decay rate is proportional to velocity, yielding an exponential function.
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