Question

Use a minimum of 4 significant figures in all calculations, and round and report your answers to 3 significant figures. Give complete answers - magnitude, units, and direction for vectors. Xity Box your answers (30 pts.) The car B turns such that its speed is increased at a rate given by a = 0.5e' m/s?, where t is in seconds. If the car starts from rest at t 0, determine the magnitudes of its velocity and acceleration when t =2 s. (30) 1. B ac = 0.se ms 0.5e mis2 5 m teo Ae= 0.se 3,atms 10t 0.5e- 0.5 e 0.5

Answer 1

Given a_t = 0.5 e^t m/s^2 ---(1) r = 5m t = 2sec (1) can be written as a_t = dv/dt or dv a_t dt dv = 0.5 e^t . dt integrating both sides v = 0.5 integral^t_0 e^t dt v = 0.5 (e^t - 1) at t = 2sec v = 0.5 (e^2 - 1) v = 3.1945 m/s---(2) Now at t = 2 sec a_t = 0.5 e^2 a_t = 3.695 m/s^2---(3) Now the normal component a_n = v^2/r a_n = (3.1945)^2/5 a_n = 2.042 m/s^2 ---(4) the resultant acceleration a = squareroot (3.695)^2 + (2.042)(from (3) and (4)) a = 4.22 m/s^2