To find the magnitude of the car's acceleration, we can use the formula for acceleration, which is defined as the change in velocity divided by the time taken:

$a = \frac{\Delta v}{\Delta t}$

Where:

• $a$ is the acceleration,
• $\Delta v$ is the change in velocity,
• $\Delta t$ is the time over which the change occurs.

Step 1: Calculate the change in velocity

$\Delta v = v_f - v_i$ Where:

• $v_f$ is the final velocity (50 mi/h),
• $v_i$ is the initial velocity (80 mi/h).

$\Delta v = 50 \, \text{mi/h} - 80 \, \text{mi/h} = -30 \, \text{mi/h}$

Step 2: Convert velocity from miles per hour to feet per second

We need to convert the velocities from miles per hour (mi/h) to feet per second (ft/s) to maintain standard units for acceleration. The conversion factor is:

$1 \, \text{mi/h} = 1.467 \, \text{ft/s}$

Thus: $v_i = 80 \, \text{mi/h} \times 1.467 = 117.36 \, \text{ft/s}$ $v_f = 50 \, \text{mi/h} \times 1.467 = 73.35 \, \text{ft/s}$

Now, calculate the change in velocity in ft/s: $\Delta v = 73.35 \, \text{ft/s} - 117.36 \, \text{ft/s} = -44.01 \, \text{ft/s}$

Step 3: Calculate the acceleration

The time interval given is 3.0 seconds, so we can now find the acceleration:

$a = \frac{-44.01 \, \text{ft/s}}{3.0 \, \text{s}} = -14.67 \, \text{ft/s}^2$

Step 4: Find the magnitude of the acceleration

Since acceleration is a vector and we are asked for the magnitude, we take the absolute value:

$|a| = 14.67 \, \text{ft/s}^2$

Thus, the magnitude of the car's acceleration is 14.67 ft/s².

Would you like more details on this, or do you have any questions?

Here are some related questions you could explore:

1. How would the acceleration change if the car slowed down over 5 seconds instead?
2. What would be the car's speed after 2 seconds of deceleration?
3. How would the acceleration be affected if the car started at a speed of 100 mi/h instead of 80 mi/h?
4. What is the relationship between velocity and acceleration during constant deceleration?
5. How would the acceleration change if the car came to a complete stop?

Tip: When converting units, always make sure to align the units properly before performing calculations to avoid errors.