91Ó°ÊÓ

When studying kinematics, the equations of motion are a great tool to predict how objects move. These equations relate an object's speed, acceleration, and distance traveled over time.
The equation used in this exercise to find the car’s acceleration is the second equation of motion:

• \(v^2 = u^2 + 2as\)

Where:

• \(v\) is the final velocity,
• \(u\) is the initial velocity,
• \(a\) is the acceleration,
• \(s\) is the displacement.

This equation tells us how change in velocity is related to acceleration and distance. It's particularly useful when the time duration isn't known. In our scenario, the car comes to a complete stop, so \(v = 0\), making it straightforward to solve for acceleration using the given initial speed and distance.
Understanding how to apply these equations can unravel many real-world motion problems.

One vital step in physics problems is ensuring all measurements are expressed in the correct unit of measure, specifically in SI units, which is the standard system used worldwide. In our exercise, the initial speed was given in kilometers per hour, but physical equations involving meters and seconds are typically used.
To convert from kilometers per hour (km/h) to meters per second (m/s):

• Multiply by \(\frac{5}{18}\)

Hence:

• 90 km/h becomes \(90 \times \frac{5}{18} = 25 \text{ m/s}\)

Likewise, always check that other values such as distance and time are in meters and seconds respectively. Making these conversions upfront eases calculation and avoids errors during the process.
By mastering unit conversion, complex problems become simpler, improving accuracy in calculations.

Acceleration is a key concept in understanding motion, defined as the rate of change of velocity. In the exercise, we calculated acceleration for a car decelerating to a stop.
To find the acceleration, we used the rearranged equation of motion:

• \(a = \frac{v^2 - u^2}{2s}\)

Here, the final velocity \(v\) is 0 (since the car stops), initial velocity \(u\) is 25 m/s, and displacement \(s\) is 40 meters.
Substituting these values in, the arithmetic works out to:

• \(a = \frac{0 - 625}{80} = -15.625 \text{ m/s}^2\)

The result is negative, showing it’s a deceleration (or negative acceleration), meaning the car is slowing down. Acceleration provides insight into how quickly an object speeds up or slows down, a crucial factor in designing and engineering for real-world applications.