A car is traveling at 20.0 m / s when the driver slams on...

A car is traveling at $20.0 \mathrm{~m} / \mathrm{s}$ when the driver slams on the brakes and brings it to a straight-line stop in $4.2 \mathrm{~s}$. What is the magnitude of its average acceleration? The defining scalar equation is $a_{a v}=\left(v_{f}-v_{i}\right) / t$. Note that the final speed is zero. Here the initial speed is greater than the final speed, so we can expect the acceleration to be negative: $$a_{a v}=\frac{0.0 \mathrm{~m} / \mathrm{s}-20.0 \mathrm{~m} / \mathrm{s}}{4.2 \mathrm{~s}}=-4.76 \mathrm{~m} / \mathrm{s}^{2}$$ Because the time is provided with only two significant figures, the answer is $-4.8 \mathrm{~m} / \mathrm{s}^{2}$.

A car is traveling at $20.0 \mathrm{~m} / \mathrm{s}$ when the driver slams on the brakes and brings it to a straight-line stop in $4.2 \mathrm{~s}$. What is the magnitude of its average acceleration?
The defining scalar equation is $a_{a v}=\left(v_{f}-v_{i}\right) / t$. Note that the final speed is zero. Here the initial speed is greater than the final speed, so we can expect the acceleration to be negative:
$$a_{a v}=\frac{0.0 \mathrm{~m} / \mathrm{s}-20.0 \mathrm{~m} / \mathrm{s}}{4.2 \mathrm{~s}}=-4.76 \mathrm{~m} / \mathrm{s}^{2}$$
Because the time is provided with only two significant figures, the answer is $-4.8 \mathrm{~m} / \mathrm{s}^{2}$.

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Key Concepts

Sign Conventions in Acceleration

Acceleration is a vector quantity, meaning its sign indicates the direction of the acceleration relative to a chosen frame of reference. A negative acceleration (often referred to as deceleration) signifies that the object is slowing down or changing direction in a way opposite to the defined positive direction.

Significant Figures

Significant figures reflect the precision of measured values in physical calculations. Using the appropriate number of significant figures in the final result ensures that the answer properly represents the precision of the initial measurements, which is essential for maintaining accuracy in scientific reporting.

Average Acceleration

Average acceleration is defined as the change in velocity divided by the time interval over which the change occurs. This key concept in kinematics quantifies how quickly an object’s speed or direction is changing with respect to time.

Change in Velocity

The change in velocity is calculated by subtracting the initial velocity from the final velocity. It is a vector quantity that represents not only the magnitude of the speed change but also its direction, which is crucial when determining the characteristics of the acceleration.

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