Find the value of ##T## and distance of particle in the first ##4## seconds

AI Thread Summary
The discussion centers on understanding the sign convention in kinematic equations, specifically why the initial upward velocity is treated as negative when the downward direction is considered positive. The calculations show that the total time for the particle's motion is 3 seconds, with 1.5 seconds spent ascending and 1.5 seconds descending. The distance traveled upwards is calculated as approximately 11.025 meters, while the distance traveled downwards is about 30.625 meters, leading to a total distance of approximately 41.7 meters. The choice of direction for velocity does not affect the results as long as the conventions are applied consistently. The key takeaway is that both upward and downward motions can yield the same results with proper sign usage.
chwala
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Homework Statement
See attached. (question with solution)
Relevant Equations
Mechanics
1711620715468.png


solution is here;

1711620751293.png


I just need to understand this part ##14.7 = -14.7 =9.8T##... why initial velocity upwards is a negative value? or i am interpreting it wrongly.

...........
In my reasoning,

##v=u+at##
##0=14.7 + (-9.8)t##
## t_1=1.5##

in reverse direction, from top to start point ##T##,

##14.7=0+9.8t##
##t_2=1.5##

##T=1.5+1.5=3##seconds

For second part i have the equation,

particle moving up vertically,

##v^2=u^2+2as##

##0 = 14.7^2 + (2× -9.8s)##
##216.09=19.6s##
##s=11.025##m

and for particle moving downwards,

##v=u+at##
##v=0 + 9.8× 2.5##
##v=24.5##

##24.5^2=0+19.6s##

##s=30.625##m

thus ##s_{total} = 11.025+30.625=41.65≅41.7 ##m
 
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chwala said:
I just need to understand this part 14.7=−14.7=9.8T... why initial velocity upwards is a negative value?
It's ##14.7=-14.7+9.8T##.
Assuming these are values substituted into ##v=v_o+at## we have ##v=+14.7##, ##v_o=-14.7##, and ##a=+9.8##. Evidently the author has chosen the downward direction to be positive, thus the initial upward velocity is negative.
 
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… and physics does not care which direction you consider positive. The author chose down as the positive direction, you chose up. Both conventions give the same result as long as you are consistent.
 
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