A 0.5 kg ball is thrown vertically upward at a speed of 25 m/s. Its velocity, v(t) (in m/s), at time, t (in seconds), is given by v(t)= 25-9.8t
Its kinetic energy, K(v) (in Joules), is given by K(v)=0.5v^2.
Express the ball's kinetic energy as a function of time, K(t).
K(t)=0.5(25-9.8t)^2
2.) Write the equation of the circle in the standard form. Find the center, radius, intercepts & graph the circle.
X^2 + y^2 + 16x -18y +145=25 = (x + 6)^2 + (y-7)^2 =25 = standard form
To express the ball's kinetic energy as a function of time, K(t), we need to substitute the expression for velocity, v(t), into the equation for kinetic energy, K(v).
Given:
v(t) = 25 - 9.8t (equation for velocity)
K(v) = 0.5v^2 (equation for kinetic energy)
To find K(t), we replace v in K(v) with v(t):
K(t) = 0.5(25 - 9.8t)^2
Now we can simplify the expression:
K(t) = 0.5(625 - 49t + 96.04t^2)
K(t) = 0.5(96.04t^2 - 49t + 625)
Therefore, the ball's kinetic energy as a function of time, K(t), is given by:
K(t) = 48.02t^2 - 24.5t + 312.5