An electron's position is given by r = 4.00t i - 6.00t^2 j + 5.00 k, with t in seconds and r in meters. In unit-vector notation, what is the electron's velocity? (Answer in terms of i, j, k, t.)What is v in unit-vector notation at t = 8 seconds? What is the magnitude of v at t = 8 seconds? What angle does v make with the positive direction of the x axis at t = 8 seconds?
velocity= dr/dt= 4i-12tj
angle= arctan -12t/4
In unit-vector notation, what is the electron's velocity v(t)? (Answer in terms of i, j, k, and t.)
The electron's velocity vector v(t) is given by the derivative of the position vector r(t) with respect to time t.
Given r(t) = 4.00t i - 6.00t^2 j + 5.00 k, we can differentiate each component with respect to time:
v(t) = dr(t)/dt = d(4.00t i)/dt - d(6.00t^2 j)/dt + d(5.00 k)/dt
The derivative of a constant multiplied by a vector component is simply the derivative of the constant multiplied by the vector component:
v(t) = 4.00 i - 12.00t j + 0 k
Therefore, in unit-vector notation, the electron's velocity v(t) is given by v(t) = 4.00 i - 12.00t j + 0 k.