# Finding displacement and time from velocity and acceleration

#### Jaycee

1. Homework Statement
He decelerates uniformly at a rate of -5.00m/s^2 over from a velocity of 7.5m/s to rest. Find the time and displacement.

2. Homework Equations
Vf^2=Vo^2 + 2a(displacement)

3. The Attempt at a Solution
0=56.25+2(-5)x is this the right way to find displacement? Solving for the x?

For time would it be 0 = 7.5 + (-5)(t) which is 1.5? That doesn't really seem correct I'm confused.

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#### Orodruin

Staff Emeritus
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For time would it be 0 = 7.5 + (-5)(t) which is 1.5? That doesn't really seem correct I'm confused.
Why do you think it is not correct?

#### Chestermiller

Mentor
The time is done correctly. The displacement is not. That's because you chose the wrong equation. What is the equation that relates the displacement to the initial velocity, the acceleration, and the time?

Chet

#### Jaycee

The time is done correctly. The displacement is not. That's because you chose the wrong equation. What is the equation that relates the displacement to the initial velocity, the acceleration, and the time?

Chet
Ok so if I did 1/2 (Vf + Vo)t would that be the correct one?

#### Jaycee

Why do you think it is not correct?
I don't really know it just seemed so short

#### Chestermiller

Mentor
Ok so if I did 1/2 (Vf + Vo)t would that be the correct one?
That would be OK to use. I was thinking more of $V_0t+\frac{1}{2}at^2$, which would give the same answer.

#### IntelvsAMD

Using this formula:
$$2a(\Delta x) = V_x^2 - V_0^2$$
Divide $2a$ to the other side
$$x - 0 = \frac{(0^2 - (7.5m/s)^2)}{(2(-5m/s^2))}$$
$$x = \frac {-56.25m^2/s^2}{-10m/s^2}$$
Units:
$$m = \frac {m^2}{s^2} * \frac{s^2}{m}$$
Left with meters:
$$x = 5.625m$$

As far as with your time, does it make sense that you're starting out at 7.5 m/s and when one decelerates at $-5.0m/s^2$, it happens decently fast?
Using: $V_x = a_xt + v_{0x}$
@ 0.5s, $V_x$ = 5m/s
$V_x = (-5m/s^2)*0.5s + 7.5m/s$​
@ 1s = 2.5 m/s
$V_x = (-5m/s^2)*0.5s + 7.5m/s$​
@ 1.5s = 0
$V_x = (-5m/s^2)*0.5s + 7.5m/s$​

Last edited:

#### gneill

Mentor
@IntelvsAMD : Be careful about providing complete solutions to other's problems: it's against Physics Forum rules. You may give hints, suggestions, point out errors and so on, but the questioner must do their own homework and hopefully in the process learn how to do it themselves in future.

"Finding displacement and time from velocity and acceleration"

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