CALC? The position of the front bumper of a test car under microprocessor control is given by x(t) = 2.17 m + (4.80 m/s2)t2 - 1 0.100 m/s6)t6. (a) Find its position and acceleration at the instants when the car has zero velocity. (b) Draw x-t , vx-t , and ax-t graphs for the motion of the bumper between t = 0 and t = 2.00 s.

Solution 18E (a).To find x position of something at time T,the formula is: 2 x(t) = 0 + v0 * t + (1/2)at Where x =i0itial position v0=initial velocity in x-direction a=acceleration t=time x(t) = 2.17 + (4.80 m/s )t (0.100)t (m) 5 5 v(t) = x(t) = 2*(4.80) t* 6 (0.*00)t = (9.6 )t (0.600)t (m/s) 4 4 a(t) = v(t) = x"(t) = 9.6 5*0.6t = 9.6 3t Position at the instants when the car has zero velocity. v(t) = t*(9.6 0.6t ) = 0 t = 0 and 0.6t = 9.6 t = 0 and t = 4.2 t = 0 and t = 1.54 first instant (t = 0) x(0) = 2.17 m second instant (t = 1.54) x(1.54) = 15 m Acceleration at the instants when the car has zero velocity. first instant(t = 0) a(0) = 9.6 m/s 2 second instant(t = 1.54) a(1.54) = 38.4 m/s 2 (b). x(t) = x(0) = 2.17 m x(t) = x(1) = 6.87 m x(t) = x(2) = 14.97 m v(t) = v(0) = 0 v(t) = v(1) = 9.0 m/s v(t) = v(2) = 0m/s a(t) = a(0) = 9.6 m/s 2 a(t) = a(1) = 6.60 m/s 2 a(t) = a(2) = 38.4 m/s 2 The time -displacement graph is plotted below. Time-velocity graph is plotted below. Time-acceleration graph is plotted below.