Newtons law of motion

Question

If impulse varies with time as I= 20t²-40t. The change in momentum is minimum at

time=

1. 2s

2. 1s

3. 1/2s

4. 3/2s

Answer 1

1). Take a derivative and set to zero.

 

OR

 

2). It's a parabola.  Find the lowest point.

Answer 2

Impulse = F·Δt = Δp/Δt · Δt = Δp = change of momentum

 

I = Δp = 20t² - 40t

 

This is a quadratic equation whose graph is a parabola that opens upward.  The minimum value of Δp will occur at the vertex of the parabola.  Convert the equation to the vertex form by completing the square:

 

Δp = 20(t² - 2t + 1) - 20

Δp = 20(t-1)² - 20

 

The vertex is at the point (1, -20) so the answer is t = 1 sec.