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Home Newtonian Physics Vectors and Motion Examples The second derivative of a vector  
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The second derivative of a vectorTwo objects have positions as functions of time given by the equations
and
Find both objects' accelerations using calculus. Could either answer have been found without calculus? Taking the first derivative of each component, we find
and taking the derivatives again gives acceleration,
The first object's acceleration could have been found without calculus, simply by comparing the x and y coordinates with the constantacceleration equation Δx = v_{o}Δt + 1/2aΔt^{2}. The second equation, however, isn't just a secondorder polynomial in t, so the acceleration isn't constant, and we really did need calculus to find the corresponding acceleration.


Home Newtonian Physics Vectors and Motion Examples The second derivative of a vector 