Answer :
Final Answer:
The average acceleration of the car during braking is approximately -3.6 m/s².
The average acceleration of the car during braking is calculated to be approximately -3.6 m/s², indicating its deceleration. This value reflects the rate at which the car's velocity decreases while coming to a stop.
Explanation:
During an emergency stop, the car's initial velocity is 24 m/s, and it comes to a complete stop after traveling a distance of 19.2 meters. To calculate the average acceleration, we can use the kinematic equation:
[tex]\[ v_f^2 = v_i^2 + 2a d \][/tex]
Where:
[tex]- \( v_f \) = final velocity (0 m/s, as the car stops)[/tex]
[tex]- \( v_i \) = initial velocity (24 m/s)[/tex]
[tex]- \( a \) = average acceleration (what we're trying to find)[/tex]
[tex]- \( d \) = distance traveled during braking (19.2 m)[/tex]
Solving for [tex]\( a \):[/tex]
[tex]\[ 0^2 = (24)^2 + 2a \cdot 19.2 \][/tex]
[tex]\[ 0 = 576 + 38.4a \][/tex]
[tex]\[ a = -\frac{576}{38.4} \][/tex]
[tex]\[ a \approx -3.6 \, \text{m/s}^2 \][/tex]
This negative value indicates deceleration, which is expected since the car is slowing down.
In this calculation, we used the kinematic equation to relate initial velocity, final velocity, acceleration, and distance traveled. This equation is derived from the basic principles of motion and can be applied to various scenarios involving uniformly accelerated motion. The negative sign of the acceleration indicates that the car is slowing down. It's important to note that this average acceleration represents the overall change in velocity over the entire braking distance.
Real-world factors such as friction, air resistance, and the characteristics of the braking system can influence the actual deceleration experienced by the car. Understanding average acceleration is crucial for analyzing the dynamics of moving objects and ensuring safety in scenarios like emergency stops.
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