or insignificant and only force acting on a falling body is the force of gravity, we call the way the body falls is a free fall. - - An object thrown at time t = from initial height s with initial velocity v satisfies the equation. g v gt v s gt v t s = − = − = − where, g = / s or ft / s . A few examples of quantities which are the rates of change with respect to some other quantity in our daily life are given below: .
Slope is the rate of change in vertical length with respect to horizontal length . . Velocity is the rate of displacement with respect to time . .
Acceleration is the rate of change in velocity with respect to time . . The steepness of a hillside is the rate of change in its elevation with respect to linear distance . Consider the following two situations: • A person is continuously driving a car from Chennai to Dharmapuri.
The distance (measured in kilometre) travelled is expressed as a function of time (measured in hours) by D t ( ) . What is the meaning one can attribute to ′ D ( ) ? It means that, “the rate of distance when t = is kmph” . • A water source is draining with respect to the time t .
The amount of water so drained after t days is expressed as V t ( ) . What is the meaning of the slope of the tangent to the curve V t ( ) at t = is − ? It means that, “the water is draining at the rate of units per day on day ” . Likewise the rate of change concept can be used in our daily life problems.
Let us now illustrate this with more examples. Example . The temperature T in celsius in a long rod of length m, insulated at both