CALC A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by x(t) = bt2 - ct3, where b = 2.40 m/s2 and c = 0.120 m/s3. (a) Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s. (b) Calculate the instantaneous velocity of the car at t = 0, t = 5.0 s, and t = 10.0 s. (c) How long after starting from rest is the car again at rest?

Solution 7E Step 1 : Let us consider the data given Function condition x(t) = bt ct 2 3 2 b = 2.40 m/s c = 0.120 m/s 3 Step 2 : We shall consider the time interval t=0 to t=10.00 s Substituting the values in the condition to find initial and final distances For t=0 s x (0) = 2.40 m/s (0) 0.120(0) m/s 3 3 i xi(0) = 0 m For t=2.00 s 2 2 3 3 x f10.0s) = 2.40 m/s (10) 0.120(10) m/s 2 3 x f10.0s) = 2.40 m/s (100) 0.120(1000) m/s x (10.0s) = 240 m/s 120 m/s = 120 m/s f Step 3 : To find the average velocity of the car xfxi V avg = tfi Substituting the values we get V avg = 1210.000 = 12 m/s