When will the skier come to a stop?

[aksarb]

Homework Statement

A skier is going 8.2m/s when she falls and starts sliding down the ski run. After 3.0s, her velocity has changed to 3.1m/s. How many seconds after she originally fell did she finally come to a stop? (Assume constant acceleration)

Homework Equations

Δd = 1(v1+v2)Δt
2
2aΔd = v2^2 - v1^2

Δd = v1 Δt + 1/2 a (Δt)2

Δd = v2 Δt - 1/2 a (Δt)2

The Attempt at a Solution

Since the question gave me 3 pieces of information, I just tired to sub it into the equations no problem. I realized afterwards that I was only going to find displacement, not the time. But, I already have time, so I have no clue how to get this question. Please help me.

 

[Kurdt]

From the information given you can find the acceleration. Once you have found the acceleration you know the initial speed (8.2 m/s) and the final speed (0 m/s) and you can then solve for time.

 

[aksarb]

So, I would have to use basically get acceleration from v2-v1 then from there use
t
t = v2-v1 to get the answer?
a

 

[Kurdt]

Sorry I missed that equation. Yes you can simply solve from the following equation knowing that the final velocity will be 0.

$$d = \frac{v_i+v_f}{2} t$$

I assumed since the question gave extra information you'd have to work out acceleration.

 

[aksarb]

Im not sure about the d. I do not have a displacement and I am not trying to find it, so how can I eliminate the d so the time can be by itself?

 

[Kurdt]

OK got confused with another thread I'm helping with.

$$v = v_0 + a t$$

You will need to solve for acceleration and then again for time.

Sorry about that.

 

[aksarb]

Ok, this question is asking for time right? So I just have to find acceleration from the information given then find time of the skier finally coming to a full stop after she originally fell?

 

[Kurdt]

Yes that should do it. I apologise for the confusion. I'm not on form tonight. I've already confused the other person with a kinematics question.

 

[aksarb]

Its ok, thanks for your help, I can finally relax :)

 

[aksarb]

The question has the following data "After 3.0s, her velocity has changed to 3.1m/s." How come I didn't have to use the 3.0 seconds or the 3.1 m/s to get the answer?

 

[Kurdt]

The question has the following data "After 3.0s, her velocity has changed to 3.1m/s." How come I didn't have to use the 3.0 seconds or the 3.1 m/s to get the answer?

You will need to use that to find acceleration. v₀ = 8.2m/s, v = 3.1 and t = 3.

 

[aksarb]

Ok thanks. Can you check the answer for this question? I did

a=v2-v1/t
= 3.1m/s + 8.2m/s / 3.0s
= 3.8 m/s^2

t = v2-v1 / a
= 3.1m/s + 8.2 m/s / 3.8m/s^2
= 3.0s

 

[Kurdt]

Ok thanks. Can you check the answer for this question? I did

a=v2-v1/t
= 3.1m/s + 8.2m/s / 3.0s
= 3.8 m/s^2

be careful with signs.

t = v2-v1 / a
= 3.1m/s + 8.2 m/s / 3.8m/s^2
= 3.0s

Remember that when the skier comes to a rest the speed will be 0 m/s. Signs again as well.

 

[aksarb]

Should it be positive because the 8.2m/s is going down due to the regualr sign conventions as left or down being negative? I conserded the sign conventions so the speed became -8.2m/s. Since there is the negative sign, it turned into a positive.

 

[Kurdt]

If you take 8.2 away from 3.1 you will end up with a negative value for acceleration which makes sense since the skier is slowing down. When you solve for time the negative signs cancel so it all works out fine.

 

[angadsingh]

First you use V=V(initial)+at to find the acceleration. This will give you -1.71.

Then you plug that into the same equation ^ but this time you make the final velocity equal zero and just find the time.
It works out to 4.8s.

 

[angadsingh]

jus realized that this has been alredy answered...LOOL!

 

[PeterO]

Homework Statement

A skier is going 8.2m/s when she falls and starts sliding down the ski run. After 3.0s, her velocity has changed to 3.1m/s. How many seconds after she originally fell did she finally come to a stop? (Assume constant acceleration)

Homework Equations

Δd = 1(v1+v2)Δt
2
2aΔd = v2^2 - v1^2

Δd = v1 Δt + 1/2 a (Δt)2

Δd = v2 Δt - 1/2 a (Δt)2

The Attempt at a Solution

Since the question gave me 3 pieces of information, I just tired to sub it into the equations no problem. I realized afterwards that I was only going to find displacement, not the time. But, I already have time, so I have no clue how to get this question. Please help me.

In 3 seconds, her velocity reduced from 8.2 to 3.1 - she lost 5.1.
She has another 3.1 to lose; so is should take an additional (3.1/5.1) of 3 seconds to stop.