Impulse of a variable force

         

A crate of mass 2 kg2\text{ kg} lies at rest on a floor. The coefficient of static friction between the crate and floor is μs=0.3,\mu_s=0.3, and that of kinetic friction between the crate and floor is μk=0.1.\mu_k=0.1. If a horizontal force FF is applied on the crate, and the magnitude of the force changes with respect to time tt according to the equation F=3tF=3t in unit of N, what is the speed of the crate after four seconds?

Assume that gravitational acceleration is g=10 m/s2.g=10\text{ m/s}^2.

A crate of mass 2.6 kg2.6\text{ kg} is initially at rest on a frictionless inclined plane that makes a 3030^\circ angle with the horizontal. A force FF whose magnitude is F=(18t) NF=(18-t)\text{ N} with respect to time tt is exerted on the crate for five seconds in the direction up the plane. Find the approximate resulting velocity of the crate.

Assume that gravitational acceleration is g=10 m/s2.g=10\text{ m/s}^2.

An object of mass 2 kg2\text{ kg} is moving on a frictionless horizontal floor with a velocity of 1.4 m/s,1.4\text{ m/s}, in a straight line. If two consecutive forces F1=2 NF_1=2\text{ N} and F2=6 NF_2=-6\text{ N} are applied on the object for 77 and 88 seconds each, respectively, what is the resulting velocity of the object?

An airplane of mass 5000 kg5000\text{ kg} is flying straight at a constant speed of 70 m/s.70\text{ m/s}. A head wind starts to blow, and the force exerted by the wind increases 50 N50\text{ N} in magnitude every second. If the plane propels itself at a constant power, how much speed will the plane lose after ten seconds?

An object of mass 5 kg,5\text{ kg}, initially at rest, is pushed by a force FF of duration 1 s1\text{ s} whose strength varies with time according to the graph above. If a=4,a=4, what is the resulting speed of the object?

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