# Help with deriving time, velocity, displacement

## Homework Statement

A dog accelerates from 2.0 m/sec to 5.0 m/sec while covering a distance of 14.0 m. How long did this take

d=(Vi+Vf/2)t

## The Attempt at a Solution

2(-Vi-Vf)d=t

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Your algebra is off. You shouldn't be subtracting the sum of the velocities. In the equation (Vi+Vf) is being multiplied into time "t." So what should you actually do to move it to the other side?

I think I should divide it?

d=(Vi+Vf/2)t
Is this the formula to find the time ??

You have to put the acceleration in consideration ,

Try to Find the acceleration first [I think it is constant] then the time from the equations of motion with constant acceleration.

:)

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## Homework Statement

A dog accelerates from 2.0 m/sec to 5.0 m/sec while covering a distance of 14.0 m. How long did this take

d=(Vi+Vf/2)t

## The Attempt at a Solution

2(-Vi-Vf)d=t

I don't understand why you used
2(-Vi-Vf)d=t

t is not velocity/distance if there is acceleration.

I am assuming the acceleration to be a constant here. Use the laws of motion to find the acceleration. Once acceleration is determined it is easy to find how long the dog took to reach a final velocity.

Sorry. A small correction in my previous reply.
t is not velocity*distance.

Sorry. A small correction in my previous reply.
t is not velocity*distance.
This is the answer according to my teacher

t=d/(Vf+Vi/2)

haruspex
Homework Helper
Gold Member
You have to put the acceleration in consideration ,
Seems like RachaelA has been taught to use the average velocity, being merely the average of initial and final velocities in the case of uniform acceleration. So no need to calculate the acceleration as such.
d=(Vi+Vf/2)t
Please use parentheses correctly. What you have written means $d = \left(V_i+\frac{V_f}{2}\right)t$, but I hope you mean $d = \left(\frac{V_i+V_f}{2}\right)t$, which you could have written as d=((Vi+Vf)/2)t.
I think I should divide it?
Yes.
This is the answer according to my teacher
t=d/(Vf+Vi/2)
Again, I hope you mean $t = \frac d{\left(\frac{V_i+V_f}{2}\right)}$ (which can be simplified a little, but no matter).
If so, dividing would have produced that.