# Negative time in equations of motion

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1. May 6, 2015

### beck blackfire

1. The problem statement, all variables and given/known data
My teacher keeps saying we can't have negative times because they don't exist and when I do these questions I get negatives and can't understand them at all, can someone help me?
1. How long does it take to slow a car from 10m/s to rest at a rate of -1.75m/s^2?
2.How long does it take to slow a car going 35m/s to 15m/s at an acceleration of -3.75m/

2. Relevant equations
t=v/a

3. The attempt at a solution
1)t=v/a
t=10/-1.75
t=-5s
2) I can't understand it almost at all

2. May 7, 2015

### paisiello2

In the use of your formula are you assuming the velocity is constant? Is this the case?

3. May 7, 2015

### Staff: Mentor

Actually it should be t=Δv/a. What is Δv?

4. May 7, 2015

### BvU

And it gets even better: $a = {\Delta v\over \Delta t}$ is the right way to memorize. Any of them can be negative.

Teacher wants to keep things easy for your sake. "negative times" is too fuzzy. Time is running forward only. Time differences can be negative -- depending on when you pin down the zero of your clock (or calendar).

5. May 7, 2015

### CWatters

In case you don't know what "Δ" means....

What others have said. Your relevant equation is really...

Acceleration = Change in velocity / Change in time.

Rearrange that to..

Change in time = Change in velocity / Acceleration

If you apply that to the problem carefully you get a +ve answer....

The change in velocity is 0-10 = -10m/s so the equation becomes..

Change in time = -10 / -1.75 = +5.7 seconds.

Try doing problem 2.

Last edited: May 7, 2015
6. May 7, 2015

### SammyS

Staff Emeritus
It's likely that your problem arises from problems which are quadratic in time.

Then you often have two solutions, with one of them possibly being negative.

For instance:
A ball is tossed upward with a speed of 50m/s from a height of 15m above ground level. How long does it take the ball to land on the ground?​

There will be two answers for time, t. One is negative.

7. May 8, 2015

### BvU

Dear Sam, from post #1 I estimate we are in an earlier stage here...
Better poster works on exercise 2

Last edited: May 8, 2015
8. May 8, 2015

### SammyS

Staff Emeritus
Point well taken.