Answer to Question #286064 in Mechanical Engineering for dyreen

Question

A particle moves on the path of 20 ft radius so that its arc distance from a fixed point on the path is given by s= 4³-10t where s is in feet and t in seconds. Compute the total acceleration at the end of 2 sec.

Answer 1

s = 4t³ - 10t

v = ds/dt = 12t² - 10

a_t​ = dv/dt = 24t

(a_t)_t=2​ = 48

a_R​ = V²/R = (V_t=2)²/20 = 48²/20 = 115.2

​​a = (a_t² + a_R²)^1/2 = (48² + 115.2²) = 124.8 ft/sec