The position of a 55 g oscillating mass is given by x(t)=(2.0cm)cos(10t), where t is in seconds. determine the velocity at t=0.40s

For this problem, we combine the concepts learned in physics and in calculus. The velocity, by definition, is the total distance travelled per time elapsed. It can also be expressed in Δx/Δt, This is also a definition in calculus where dx/dt is equal to velocity. Therefore, to solve the velocity, differentiate the equation in terms of t.

x = 2 cos(10t)
dx/dt = 2*(-sin(10t))*(10)
dx/dt = -20sin (10t)

We are asked to find the velocity at 0.40 seconds. Thus, we substitute t = 0.40 to the equation

dx/dt = -20sin(10*0.4)
dx/dt = v = -1.395 m/s

Therefore, the velocity at t=0.04 seconds is -1.395 m/s. The negative sign connotes that the direction of the motion is south or to the left based on the sign convention.

If there was no gravity then their would be no downword force on the football to have it return the the grownd, and if there was no friction (mainly air friction) then there would be no opposing force the stop the ball from moving through the air allowing the ball to travle ∞.