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In this lesson, we will learn how to solve problems using Newton's second law for a body of variable motion and/or one that is acted upon by a variable force.

Q1:

The mass of a body at time π‘ is given by π ( π‘ ) = ( 2 π‘ + 1 2 ) k g , whereas its position vector is r c ( π‘ ) = οΉ 2 π‘ + 3 π‘ + 1 5 ο 2 , where c is a constant one vector, r is measured in meters, and π‘ is measured in seconds. Find the magnitude of the force acting on the body at π‘ = 2 seconds.

Q2:

The mass of a body at time π‘ is given by π ( π‘ ) = ( 3 π‘ + 1 0 ) k g , whereas its position vector is r c ( π‘ ) = οΉ 2 π‘ + 2 π‘ + 1 3 ο 2 , where c is a constant one vector, r is measured in meters, and π‘ is measured in seconds. Find the magnitude of the force acting on the body at π‘ = 2 seconds.

Q3:

A body of mass 11 kg started moving along the π₯ -axis at an initial velocity 8 m/s in the direction of π₯ increasing. After time π‘ seconds, where π‘ β₯ 0 , the bodyβs velocity was π£ m/s in the same direction, and the force acting on the body was πΉ = οΌ 4 6 π£ + 6 ο N . Determine the value of π‘ at which π£ = 1 0 / m s .

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