: Velocity is the first derivative of position ( ) with respect to time ( Step 2: Defining Instantaneous Acceleration
But did you travel at exactly $50\text km/h$ the entire time? Of course not. You stopped at traffic lights, you accelerated on the highway, and you slowed down for tolls. If a police officer wanted to fine you for speeding at a specific moment, say, exactly 2 hours and 15 minutes into the journey, the "average speed" is useless. They need your speed . derivatives class 11 physics
[ v(t) = \fracdsdt = \fracddt(4t^2) + \fracddt(3t) + \fracddt(2) ] [ v(t) = 8t + 3 ] At ( t = 2 ): [ v = 8(2) + 3 = 19 , \textm/s ] : Velocity is the first derivative of position
[ \fracddx(x^n) = n x^n-1 ] Displacement ( s(t) = 5t^3 ) Velocity ( v = \fracdsdt = 15t^2 ) If a police officer wanted to fine you
Let’s solve a typical Class 11 problem using derivatives.
In physics, a derivative represents the of one quantity with respect to another. Class 11 applications include: