The Problems

Consider a problem say A car is running 5 m/s on road for 5 seconds. If calculate the acceleration $$ a = \frac{v-u}{t} $$ we get $a = 0 m/s^2$ But if we do this $$ t = \frac{v-u}{a} $$ we get t as infinity or not defined Similary few formulae become useless beyond a certain range. How can we tackle this problem? there are too many formulae and every formula is limited **Or can we write to find acceleration we first subtract final velcoity by initial velocity and the total is divided by time Also the formula is not applicable for finding the time when the velocity is uniform Better still we can write time cannot be found by substracting final velocity by initial velocity and the total divided by acceleration in cases where velocity is uniform** Similar types of problem also methods to solve for time is given in standard school textbook may not be in today's time Such formulae create unsettling doubt in the mind of the pupil which contradicts the belief that (if someone m...

Today I was solving the equations of quantum mechanics from the book written by Sir David J. Griffith And the old question lingered around my mind Why do we need to use? $$ e^{i\theta} = \cos\theta + i\sin\theta $$ because e (exponential) is a value and angle raise to e makes no sense. Even if it does then \[ \begin {align*} & i\theta = \ln ({\cos\theta + i\sin\theta}) \\ \\ & \theta = \frac{\ln( {\cos\theta + i\sin\theta})}{i} \\ \\ & {\theta}^2 =-(\ln ({\cos\theta + i\sin\theta}))^2 \\ \\ \text {But we know that} \\ \\ & {\theta}^2 \neq -(\ln ({\cos\theta + i\sin\theta}))^2 \\ \\ \end {align*} \]