In a kinematics question, where a ball is thrown up and it comes down and we have to calculate the total time for it, we can find it by breaking the motion into two parts, 1) going upwards, 2) going downwards, and then add each of their times to get total, BUT there is another, much more simpler way, where we can use s = 1/2 at² + ut just once for the whole motion, but how does that work? Coz acceleration changes from -g to +g when the ball changes direction, but we use only -g in the eq, and SUVAT eqs' requirement is that acc mustn't change.
Kinematics – How Can One Equation Be Used for Both Motions?
kinematics
Best Answer
No, the acceleration does not change. It's 9.8 m/s/s [down] on the way up and 9.8 m/s/s [down] on the way down.
In solving these sorts of accelerated motion problems one of the initial steps is decide which will be the positive direction. It's good practice to state this explicitly.
Say we chose up as positive, then, for the projectile in question, initial velocity will be positive and acceleration will be negative. The displacement will be positive if we are just considering the motion on the way up, or it will be zero if we are considering the whole up and down travel.
I suspect what you did when you solved for the time going up and the time coming down separately is that going up you took up as positive and going down you picked down as positive. Since the acceleration is always down that would explain why it was negative for the first calculation and positive for the second.