Does retardation have opposite sign of acceleration? For example if acceleration of a car is 15m/s² than if we are asked to report retardation will we report it as -15m/s² or simply there is a retardation of 15m/s²? Is it true even if body is accelerating (increasing magnitude of velocity)?
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3 Answers
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This is a convention question in English and has very little to do with physics.
If an object is moving faster and faster, i.e. magnitude of velocity (i.e. speed) is increasing, then under no circumstance do you call any of that a retardation. There is no such thing as a negative retardation. You are simply supposed to refuse to characterise it as a retardation.
If, and only if, $-\vec a\cdot\frac{\vec v}{|\vec v|}>0$ do you talk about this positive non-zero quantity as retardation. Otherwise, you only refer to the acceleration as it is.
answered May 23 at 15:25
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Acceleration is a vector, so it can be either positive or negative, depending on your coordinate system. If my car's speed is increasing by $1(m/s)$ every second and my positive $x$ axis is located, say, in $(1,0)$ then my acceleration vector is $\vec{a}=1(1,0) m/s^2$. If I now start decreasing my car's velocity, then my acceleration is pointing in the opposite direction as in the former case, and therefore it is now $\vec{a}=-1(1,0)m/s^2$.
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Noting that acceleration has a plus/minus sign only in straight-line motion, observe that
for a particle with initial velocity $-20$m/s and constant acceleration $15$m/s², its speed at around the first second must be decreasing (that is, at $t=1$s the particle must be retarding) at $15$m/s²
a car initially at rest subject to a constant $−15$ m/s acceleration is speeding up at $15$ m/s².
These examples show that retardation and acceleration need not have opposite signs. The plus/minus sign of the particle's acceleration indicates the direction of the net force acting on the particle, while the plus/minus sign of the particle's retardation indicates whether the particle is slowing down.
