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# NTSE Study Tips on Free Fall Equations - Part-1

Many a student find free fall equations tough, but the students at STEPS (A program run by TCY in Ludhiana, Ambala, Jammu, Karnal and Kurukshetra for NTSE and NSEJS aspirants) just solve the toughest of free fall problems mentally. I would like to share their secret with you.

The first basic principle is the time taken for a change in velocity under uniform acceleration is given by, “change in velocity/acceleration”

The second principle is that when you throw a ball up with a velocity of say 20 m/s, then it returns back with a velocity -20 m/s. So the change in velocity is 40 m/s in the direction of acceleration. To simplify things the change in velocity is simply double the initial velocity.

Using these two principles let us try to calculate time of flight of a ball thrown up with a speed of 25 m/s.

Change in velocity =50 m/s

Acceleration = 10 m/s^2

Time = 5 s

Now isn’t that easy!

Attempt more questions to practice and prepare for NTSE exam @ https://www.tcyonline.com/exam-preparation-ntse-olympiad-preparation-and-practice-test/100194/ntse-nsejs-kvpy

Keep visiting TCYonline.com for more Tips and Strategies on NTSE exam.

# NTSE Study Tips on Free Fall Equations - Part-2

Once we have mastered the art of calculating time of flight (refer to part-1), we just need two more principles to calculate total distance mentally as STEPS students do.

Principle 3: the time required to reach max height is half the time of flight.

Principle 4: The average velocity under uniform acceleration is average of initial and final velocities. Since the final velocity is zero, the average velocity is simply half of initial velocity.

Now let us calculate the maximum height of a ball projected up with a speed of 30 m/s which is just the distance travelled up by the projectile before it stops.

Time taken to reach max height =3 s

Average speed is 15 m/s

Max height = 45 m

Isn’t that COOL STUFF! We will cover the case of projectiles in 2-D in the third part.

Attempt more questions to practice and prepare for NTSE exam @ https://www.tcyonline.com/exam-preparation-ntse-olympiad-preparation-and-practice-test/100194/ntse-nsejs-kvpy

Keep visiting TCYonline.com for more Tips and Strategies on NTSE exam.