A player throws a ball upwards with an initial speed u. Choosing x . . .

Question : A player throws a ball upwards with an initial speed u. Choosing x=0 and t=0 to be the location and time of the ball at its highest point and vertically downward direction to be the positive direction of x-axis, give the signs of position, velocity and acceleration of the ball during its upward motion. 

a) Positive, Positive, Positive

b) Negative, Positive, Negative

c) Positive, Negative, Negative

d) Positive, Negative, Positive

Doubt by Jaskirat

Solution : 

When we consider x=0 and t=0 to be the location and time of the ball at its highest point and vertically downward direction to be the positive direction of x-axis then x=0 will be considered as the final position of the body during its upward motion. 

The motion of the ball will start from some positive coordinate on the +ve direction of the x-axis. Hence, the position of the ball during its upward motion will be +ve. 

We know, velocity=displacement/time

As the ball move upward its displacement will be -ve which means that the velocity will also be -ve and it will become zero at the highest point. Hence, the velocity will be negative.

The direction of acceleration will always be in the downward direction but here the downward direction is considered as +ve x-axis. So the acceleration of the body coming downward will be +ve. 

We can also understand it like this
a=(v₂-v₁)/t
where v2 is the final velocity and v₁ is the initial velocity during its upward motion. Here both v₂ and v₁ are -ve velocities but the magnitude of v₁>v₂. so as per the above formula acceleration (a) will be positive. 

Hence, for a body moving upward, the direction, the signs of position, velocity and acceleration will be positive, negative and positive respectively. 

Hence, d) Positive, Negative, Positive, would be the correct option. 

Note : During the downward motion of the ball the signs of position, velocity and acceleration will be positive, positive and positive respectively.