A particle of mass m is at rest at t = 0. Its momentum for t 0 is given by p_x = 6t² kg m/s, where t is in s. Find an expression for F_x (t), the force exerted on the particle as a function of time.

Question

A particle of mass m is at rest at t = 0. Its momentum for t > 0 is given by p_x = 6t² kg m/s, where t is in s. Find an expression for F_x (t), the force exerted on the particle as a function of time.

Accepted Answer

Hey, everyone. So this problem is dealing with momentum. Let's see what its path means. Consider a body of mass M is stationary at time T equals zero seconds and experiences a momentum expressed as PX equals nine T cubed kilogram meters per second or T is in seconds. Obtain an equation representing the force experienced by a body. Our multiple choice answers are a three T squared newtons. B nine fourths multiplied by T to the fourth newtons C 27 T squared newtons or D nine T to the fourth newtons. So the key to this problem is recalling that Newton's second law in terms of momentum is given by F equals DP divided by DT. From the problem P, our momentum equation is nine T cubed. And so when we plug that in to our force equation, we have nine TQ multiplied by DDT. So we have to take the derivative of this momentum equation with respect to time to get our force equation. When we do that, we get 27 T squared and that is in units of mutants. So it's a pretty straightforward problem as long as we can recall that Newton's second law in terms of moment. And so that answer aligns with answer choice C and that's all we have for this one, we'll see you in the next video.

A particle of mass m is at rest at t = 0. Its momentum for t > 0 is given by p_x = 6t² kg m/s, where t is in s. Find an expression for F_x(t), the force exerted on the particle as a function of time.

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Key Concepts

Momentum

Newton's Second Law

Calculus