# Calculating the distance traveled by a ball

## Homework Statement

The start velocity of the ball is 3m/s upward direction. Ball reaches its highest point after 1.2seconds
No air or other friction like that
i need to find how far the ball has travelled after 0.4 seconds, and after 2.4 seconds

i cant get the right answers, says its supposed to be 1meter for 0.4 sec, and 3.6meter for 2.4 sec

## Homework Equations

ive tried to use v0*t + 1/2a*t2 where:
v0 = 3
t= 0.4 or 2.4
a= +/.- 2.5m/s^2

## The Attempt at a Solution

i cant get the right answers, says its supposed to be 1meter for 0.4 sec, and 3.6meter for 2.4 sec, and the equation i mentioned earlier did not work..

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Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

The start velocity of the ball is 3m/s upward direction. Ball reaches its highest point after 1.2seconds
No air or other friction like that
i need to find how far the ball has travelled after 0.4 seconds, and after 2.4 seconds

i cant get the right answers, says its supposed to be 1meter for 0.4 sec, and 3.6meter for 2.4 sec

## Homework Equations

ive tried to use v0*t + 1/2a*t2 where:
v0 = 3
t= 0.4 or 2.4
a= +/.- 2.5m/s^2

## The Attempt at a Solution

i cant get the right answers, says its supposed to be 1meter for 0.4 sec, and 3.6meter for 2.4 sec, and the equation i mentioned earlier did not work..
Where does the acceleration $a = \pm 2.5 m/s^2$ come from? (I know the answer, but you need to get into the habit of explaining your reasoning!)

Anyway, you need to show your work. WHAT do you get for $t = 0.4$ sec? (I get 1.0 m.) What do you get for $t = 2.4$ sec? We cannot possibly help you if we cannot tell where you made your errors.

Where does the acceleration $a = \pm 2.5 m/s^2$ come from? (I know the answer, but you need to get into the habit of explaining your reasoning!)

Anyway, you need to show your work. WHAT do you get for $t = 0.4$ sec? (I get 1.0 m.) What do you get for $t = 2.4$ sec? We cannot possibly help you if we cannot tell where you made your errors.
Thanks for reply, and im sorry for not beeing specific, first time posting.

What i thought i was supposed to do was to use the equation for the distance v0*t + 1/2a*t2, and put my numbers in:
3*0.4+1/2*2.5*0.4^2 i thought this would give me 1meter in answer, but i get 1.4meter

I got acceleration a=2.5m/s^2 from Δv/Δt where v is velocity and t time. v2-v1/t2-t1 = 0m-3m/s / 1,2s-0s = -3m/s / 1,2s = -2,5m/s^2

SammyS
Staff Emeritus
Homework Helper
Gold Member
Thanks for reply, and im sorry for not beeing specific, first time posting.

What i thought i was supposed to do was to use the equation for the distance v0*t + 1/2a*t2, and put my numbers in:
3*0.4+1/2*2.5*0.4^2 i thought this would give me 1meter in answer, but i get 1.4meter

I got acceleration a=2.5m/s^2 from Δv/Δt where v is velocity and t time. v2-v1/t2-t1 = 0m-3m/s / 1,2s-0s = -3m/s / 1,2s = -2,5m/s^2
OK. That makes sense for the acceleration. Even the sign makes sense.

What i thought i was supposed to do was to use the equation for the distance v0*t + 1/2a*t2, and put my numbers in:
3*0.4 + 1/2 * 2.5 * 0.4^2
i thought this would give me 1meter in answer, but i get 1.4meter
What sign should the acceleration have ?

Ray Vickson
Homework Helper
Dearly Missed
Thanks for reply, and im sorry for not beeing specific, first time posting.

What i thought i was supposed to do was to use the equation for the distance v0*t + 1/2a*t2, and put my numbers in:
3*0.4+1/2*2.5*0.4^2 i thought this would give me 1meter in answer, but i get 1.4meter

I got acceleration a=2.5m/s^2 from Δv/Δt where v is velocity and t time. v2-v1/t2-t1 = 0m-3m/s / 1,2s-0s = -3m/s / 1,2s = -2,5m/s^2
Please use parentheses: you wrote $v_2 - \frac{v_1}{t_2} - t_1$, but (I hope) you meant $\frac{v_2-v_1}{t_2-t_1}$, which you would write in plain text as (v2-v1)/(t2-t1). You need brackets because when parsing mathematical expressions, multiplication and division take precedence over addition and subtraction, so when you write v2 - v1/t2 - t1 you first compute the fraction v1/t2, then you perform subtractions. Using parentheses over-rides those priorities and gives you what you really want.

Anyway, your equation $d = 3 t + \frac{1}{2} 2.5 \, t^2$ has the acceleration pointing in the same direction as the velocity. Therefore, your ball will keep increasing its upward speed without limit, and so will blast off into outer space just like a rocket. Your ball will not reach a maximum height, it will just keep going up forever.

Last edited:
Please use parentheses: you wrote $v_2 - \frac{v_1}{t_2} - t_1$, but (I hope) you meant $\frac{v_2-v_1}{t_2-t_1}$, which you would write in plain text as (v2-v1)/(t2-t1). You need brackets because when parsing mathematical expressions, multiplication and division take precedence over addition and subtraction, so when you write v2 - v1/t2 - t1 you first compute the fraction v1/t2, then you perform subtractions. Using parentheses over-rides those priorities and gives you what you really want.
Yes thats how i ment (v2-v1) / (t2-t1).

Anyway, your equation $d = 3 t + \frac{1}{2} 2.5 \, t^2$ has the acceleration pointing in the same direction as the velocity. Therefore, your ball will keep increasing its upward speed without limit, and so will blast off into outer space just like a rocket. Your ball will not reach a maximum height, it will just keep going up forever.

If I do d=3*0.4+1/2*-2.5*0.4^2
where the acceleration now is negative instead, i get correct answer (1).

d=3*2.4+1/2*-2.5*2.4^2
however, when i try to use 2.4seconds instead, i get the answer 0 if i use -2.5 acceleration, and answer 14.4 if i use +2.5 acceleration, answer is supposed to be 3.6

d=3*1.2+1/2*-2.5*1.2^2
If i use 1.2 seconds for instance, then i see the ball travels 1.8meter, and knowing there is no friction in air or the surface, i can tell that for 2.4 seconds the distance travelled must have doubled from 1.8 meter (right)?

If the above is true, does it mean that the reason i get the answer 0 from d=3*2.4+1/2*-2.5*2.4^2 is because the ball travels 1.2meter in lets say this direction ->
Then when it turns, it falls back <- to its original state, so that it says 0, where the distance from start to finish is 0.
Im not sure if this is how it works, just thinking out loud

mjc123
Homework Helper
The question asks how far the ball has travelled - i.e. the total distance it has covered - not how far it now is from the starting point. (Perhaps it's a question of the interpretation of the English wording, for non-English speakers. But that's what it means.) So the correct method is to calculate how far it travelled up to the highest point, and how far it came down after that.

SammyS
Staff Emeritus
Homework Helper
Gold Member
...

If the above is true, does it mean that the reason i get the answer 0 from d=3*2.4+1/2*-2.5*2.4^2 is because the ball travels 1.2meter in lets say this direction ->
Then when it turns, it falls back <- to its original state, so that it says 0, where the distance from start to finish is 0.
I'm not sure if this is how it works, just thinking out loud
If you travel 3 km to the grocery store and then 3 km back home, how far have you traveled ?

mjc123
Homework Helper
Reminds me of the joke about the man who went to a railway station and asked for a return ticket.
"Where to, sir?" asked the clerk.
"Back here, you idiot!"

• Merlin3189 and SammyS
Merlin3189
Homework Helper
Gold Member
I wonder if it would help you understand, if you sketched a graph of velocity against time?
I suppose you'd have to assume that acceleration was constant, but you seem to have done that in your selection of equations.