Amotor cycle travelling at 10 m/s accelerates at 4m/s(squared) for 8s. a) what is the final velocity? b) how far does it travel during the 8s

Consider the following position function. find (a) the velocity and the speed of the object and (b) the acceleration of the object. bold r left parenthesis t right parenthesisr(t)equals=left angle 6 t superscript 4 baseline comma 2 t cubed right angle6t4,2t3 for tgreater than or equals≥0

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.

The number of passengers who arrive at the platform of a subway station for the 10 am train is a random variable with a mean of 120 and a variance of 16. find the lower bound of the probability that there will be between 100 and 140 passengers (round off to second decimal place).