Most of the important things in the world have been accomplished by people who have kept on trying when there seemed to be no help at all. – **Dale Carnegie**

# Lecture 7 Motion in a straight line

**Example 3.4** A ball is thrown vertically upwards with a velocity of 20 m s^{–1} from the top of a multistory building. The height of the point from where the ball is thrown is 25.0 m from the ground. (a) How high will the ball rise ? and (b) how long will it be before the ball hits the ground? Take g = 10 m s^{–2}.

**Example 3.5** Free-fall : Discuss the motion of an object under free fall. Neglect air resistance.

**Example 3.6** Galileo’s law of odd numbers : “The distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity [namely, 1: 3: 5: 7……].” Prove it.

**Example 3.7** 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_{0} ) 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.

**Example 3.8** Reaction time : When a situation demands our immediate action, it takes some time before we really respond. Reaction time is the time a person takes to observe, think and act. For example, if a person is driving and suddenly a boy appears on the road, then the time elapsed before he slams the brakes of the car is the reaction time. Reaction time depends on complexity of the situation and on an individual. You can measure your reaction time by a simple experiment. Take a ruler and ask your friend to drop it vertically through the gap between your thumb and forefinger (Fig. 3.15). After you catch it, find the distance d traveled by the ruler. In a particular case, d was found to be 21.0 cm. Estimate reaction time.