Exercise 2.7 a car is stopped at a traffic light. it then travels along a straight road so that its distance from the light is given by x(t)=bt2−ct3, where b = 2.60 m/s2 and c = 0.130 m/s3

The solution is:

x(t) = 3*t^2 - 0.130*t^3 
v(t) = x'(t) = 6*t - 0.360*t^2 

v(5) = 6*5 - 0.360*5^2 = 21 m/s 
v(10) = 6*10 - 0.360*10^2 = 24 m/s 
 
set v(t) = 0 and solve for t 
0 = 6*t - 0.360t^2 
0 = t*(6-0.360*t) 
6-0.360*t = 0 
t = 6/.360 = 16.7 s

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