# Sign of acceleration from position-time graph

These three graphs are from my textbook. It states that the acceleration in 1) is positive, 2) is negative and 3) is zero and can be told by looking at the slope.

What I understand from the graph is in the picture above. How can I conclude the signs of acceleration from that information in graphs 1 and 2?

• If you can understand the velocity change, can't you understand the acceleration sign? If you can't understand the former, look for slope of the graph. – Wrichik Basu Jul 30 '17 at 18:39
• I understand about velocity change and slope. Like in graph 1, velocity is changing from negative to positive. Velocity is changing so the object is accelerating. But how does that tell anything about the sign of acceleration? – Raknos13 Jul 30 '17 at 18:42
• Velocity us changing from negative to positive means that the body is accelerating, as the velocity is increasing. – Wrichik Basu Jul 30 '17 at 18:49
• I already said I knew that change in slope means the body is accelerating. What I'm interested is the sign of a! – Raknos13 Jul 30 '17 at 18:57
• If it's accelerating, then it's +a, if retarding, then -ve. – Wrichik Basu Jul 30 '17 at 19:24

## 2 Answers

The acceleration is the rate of change of velocity (i.e., how fast it's changing in time).

A positive acceleration means increasing values of velocity, for example, as in your picture, that the velocity (slope) goes from negative to positive values. A negative $a$ means decreasing values for $v$.

When the velocity is neither growing, nor getting smaller, its rate of change is zero: $a=0$.

Graphically, when a curve in the $x$ vs. $t$ plot has its concavity pointing up, $a$ is positive; when it's pointing down, $a$ is negative.

• A negative $a$ doesn't necessarily mean decreasing $v$; it only applies when $v$ is positive. If $v$ is negative, negative $a$ would mean increase in speed. – Raknos13 Jul 30 '17 at 19:02
• Numerically, it's a decrease: $-5<-3$, the speed, though, yes, would be increasing -- but speed and velocity aren't the same. – stafusa Jul 30 '17 at 19:04
• @R3l1c A negative $a$ makes $v$ more negative. This is what is meant when people say "decreasing". – Steeven Jun 2 '18 at 8:07
• @R3l1c, velocity has a sign associated with it but speed doesn't. Mathematically, if something has a negative velocity and a negative acceleration, the object is speeding up, but the velocity is decreasing (getting more negative). – David White Jul 7 '18 at 21:23

In the first graph the velocity is changing from negative to positive with respect to time, i.e. $\frac{dv}{dt} > 0$. Acceleration $a = \frac{dv}{dt}$ and thus a is positive.

In the second graph it's just the opposite.