and x ( t ) = . t . The sixth column lists the difference ∆ x = x ( t ) – x ( t ) and the last column gives the ratio of ∆ x and ∆ t , i.e. the average velocity corresponding to the value of ∆ t listed in the first column.
We see from Table . that as we decrease the value of ∆ t from . s to . s, the value of the average velocity approaches the limiting value .
m s – which is the value of velocity at t = . s, i.e. the value of dx dt at t = . s.
In this manner, we can calculate velocity at each instant for motion of the car. The graphical method for the determination of the instantaneous velocity is always not a convenient method. For this, we must carefully plot the position–time graph and calculate the value of average velocity as ∆ t becomes smaller and smaller. It is easier to calculate the value of velocity at different instants if we have data of positions at different instants or exact expression for the position as a function of time.
Then, we calculate ∆ x / ∆ t from the data for decreasing the value of ∆ t and find the limiting value as we have done in Table . or use differential calculus for the given expression and calculate dx dt at different instants as done in the following example. Example . The position of an object moving along x-axis is given by x = a + bt where a = .
m , b = . m s – and t is measured in seconds. What is its velocity at t = s and t = . s .
What is the average velocity between t = . s and t = . s ? Answer In notation of differential calculus, the velocity is - dx bt 2b t = .
t m s dt dt At t = s, v