A particle moves on a line away from its initial position so that after t hours it is s = 4t^2 + t miles from its initial position. Find the average velocity of the particle over the interval [1, 4]. Include units in your answer.

Answer:Average velocity is 21 miles/hrStep-by-step explanation:Given a particle moving away from its initial position Position after t hours that is                     s(t) = 4[tex](t^{2})[/tex] + tWe have to find the average velocity of the particle over the interval [1,4]Average velocity = [tex]\frac{Distance Travelled}{Time Elapsed}[/tex]              Distance travelled = [tex] [s]_{1}^{4}[/tex]                                              = s(4) - s(1)                                              = 4[tex](4^{2})[/tex] + 4 - 4[tex](1^{2})[/tex] -1                                              =  63 miles                 Time elapsed = 4 - 1 = 3 Average velocity = [tex]\frac{63}{3}[/tex]                              = 21 miles/hr