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).
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To express the ball's kinetic energy as a function of time, K(t), we first need to find the velocity as a function of time, v(t), and then substitute this into the formula for kinetic energy.
Given: v(t) = 25 - 9.8t
To find K(t), substitute the expression for v(t) into the formula for kinetic energy, K(v) = 0.5v^2.
K(t) = 0.5(25 - 9.8t)^2
Now, let's simplify this expression using the laws of algebra.
K(t) = 0.5(625 - 490t + 96.04t^2)
K(t) = 312.5 - 245t + 48.02t^2
Therefore, the ball's kinetic energy as a function of time, K(t), is given by the equation K(t) = 312.5 - 245t + 48.02t^2.