Question

A particle moves along a straight line with velocity given by v\left( t \right) = 5 + {5^{\frac{t}{3}}} for t \geqslant 0. What is the acceleration of the particle at time t=4?

(A) 0.422
(B) 0.698
(C) 1.265
(D) 8.794
(E) 28.381

Answer 1

a(t) = v'(t) = \frac{d}{dt} [5 + 5^{\frac{t}{3}}] = 0 + \frac{5}{3} \cdot 5^{\frac{t}{3}-1}

We are asked to find the acceleration of the particle at time t=4, so we substitute t=4 into the acceleration function:

a(4) = \frac{5}{3} \cdot 5^{\frac{4}{3}-1} = \frac{5}{3} \cdot 5^{\frac{1}{3}} \approx 1.265

Therefore, the answer is (C) 1.265.