equal intervals τ and find out the distances

traversed during successive intervals of time. Since initial velocity is zero, we have Using this equation, we can calculate the position of the object after different time intervals, , τ , τ , τ … which are given in second column of Table . . If we take (– / ) g τ as y — the position coordinate after first time interval τ , then third column gives the positions in the unit of y o .

The fourth column gives the distances traversed in successive τ s. We find that the distances are in the simple ratio : : : : : … as shown in the last column. This law was established by Galileo Galilei ( - ) who was the first to make quantitative studies of free fall. Example .

Stopping distance of vehicles : When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity ( v ) and the braking capacity, or deceleration, – a that is caused by the braking. Derive an expression for stopping distance of a vehicle in terms of v o and a . Answer Let the distance travelled by the vehicle before it stops be d s .

Then, using equation of motion v = v o + ax , and noting that v = , we have the stopping distance s = – Thus, the stopping distance is proportional to the square of the initial velocity. Doubling the Table . gt = − initial velocity increases the stopping distance by a factor of (for the same deceleration). For the car of a particular make, the braking distance was found to be m, m, m and m corresponding to velocities of , , and m/s which are nearly consistent with the above formula.

Stopping distance is an important factor considered in setting speed limits, for example, in school zones.