Why Does My Calculated Answer Differ from the Marked One on a Physics Test?

[RuthlessTB]

While I was studying I downloaded and printed a previous old test which already answered
I tried to re-solve the questions by myself but there is one question made me confused as I get a result mentioned in the options but the marked answer is different.

I am talking about question 3 in the following picture

Homework Statement

Vo= 0 m/s
V= 20 m/s
Xo= 0 m
X= 800 m
t= 25 s
a= ?

Homework Equations

1) X = Xo + Vo t + 0.5 a t^2
2) V^2 = Vo^2 + 2 a (X-Xo)

The Attempt at a Solution

I used the first equation
X = Xo + Vo t + 0.5 a t^2

solution will be
800 = 0 + 0 (25) + 0.5 a (25)^2
800 = a 312.5
-a 312.5 = 800
-a = 800/312.5 = 2.56
then I took the square root of 2.56 and I got 1.6 m/s^2
So -a = -1.6 m/s^2

Is that right or no?

 

[azizlwl]

Initial velocity is not zero.
If it starts from rest ,it will never reach positive velocity with negative accceleration.

 

[ehild]

While I was studying I downloaded and printed a previous old test which already answered
I tried to re-solve the questions by myself but there is one question made me confused as I get a result mentioned in the options but the marked answer is different.

I am talking about question 3 in the following picture

Homework Statement

Vo= 0 m/s
V= 20 m/s
Xo= 0 m
X= 800 m
t= 25 s
a= ?

Homework Equations

1) X = Xo + Vo t + 0.5 a t^2
2) V^2 = Vo^2 + 2 a (X-Xo)

The Attempt at a Solution

I used the first equation
X = Xo + Vo t + 0.5 a t^2

solution will be
800 = 0 + 0 (25) + 0.5 a (25)^2
800 = a 312.5
-a 312.5 = 800
-a = 800/312.5 = 2.56
then I took the square root of 2.56 and I got 1.6 m/s^2
So -a = -1.6 m/s^2

Is that right or no?

First you say that -a=2.56, (why minus??) and you take the square root of 2.56 and say that it is a? Why?

By the way, it is not said that the initial velocity was zero. The velocity after 25 s is 20 m/s.

ehild

 

[RuthlessTB]

Well, I thought initial velocity means Vo=0.

I tried multiple equation but couldn't get the answer, so I made a random mess up I guess.

I realized now that I need first to calculate the initial velocity then I calculate the acceleration.

I used to calculate the initial velocity this equation:
X= Xo + 0.5 (V+Vo) t
I don't know if the equation right or no but my result for initial velocity is 0.03 m/s.

Not sure if it is right or no.

 

[ehild]

I realized now that I need first to calculate the initial velocity then I calculate the acceleration.

I used to calculate the initial velocity this equation:
X= Xo + 0.5 (V+Vo) t
I don't know if the equation right or no but my result for initial velocity is 0.03 m/s.

Not sure if it is right or no.

Take Xo=0. Otherwise the equation is correct. X=800 m, V=20 m/s, t=25 s. How did you get Vo=0.03 m/s? It is wrong.

ehild

 

[RuthlessTB]

X=0.5 (V+Vo) t
800= 0.5 (20+Vo) 25
800= 12.5 (20+Vo)
800= 250+Vo
Vo+250=800
Vo=800/250= 3.2 m/s.
Is that right? If so, can you help me to find out the acceleration?

I tried using this equation
V=Vo+a t
But it gives me a different answer which is wrong.

Here what I did
V=Vo+a t^2
20=3.2+ a (25)^2
Can anyone tell me what I need to do next? My answer always different than the right answer

 

[mishek]

800= 12.5 (20+Vo)
800= 250+?Vo
Vo+250=800
Vo=800/250= 3.2 m/s.
Is that right? If so, can you help me to find out the acceleration?

Did you miss something?

 

[RuthlessTB]

I got it right now, but please check my steps if there is a mistake or not.

X=0.5 (V+Vo) t
800=0.5 (20+Vo) 25
800=12.5 (20+Vo)
Now since
12.5 (20+Vo) = 800
20 + Vo = 800/12.5
20 + Vo = 64
Vo = 64-20 = 44 m/s

Acceleration:
V= Vo + a (25)
20= 44 + a (25)
20-44= a (25)
-24= a (25)
a 25 = -24
a = (-24)/15 = -0.96 m/s^2

Do I have mistakes in my steps?

 

[ehild]

I got it right now, but please check my steps if there is a mistake or not.

X=0.5 (V+Vo) t
800=0.5 (20+Vo) 25
800=12.5 (20+Vo)
Now since
12.5 (20+Vo) = 800
20 + Vo = 800/12.5
20 + Vo = 64
Vo = 64-20 = 44 m/s

Acceleration:
V= Vo + a (25)
20= 44 + a (25)
20-44= a (25)
-24= a (25)
a 25 = -24
a = (-24)/15 = -0.96 m/s^2

Do I have mistakes in my steps?

It is correct except a typo at the end. a=-24/25=-0.96 m/s^2.

ehild