If the car’s speed decreases at a constant rate from 80  mi/h
  to 50  mi/h
  in 3.0  s
 , what is the magnitude of its acceleration, assuming that it continues to move in a straight line?

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.

If the car’s speed decreases at a constant rate from 80 mi/h to 50 mi/h in 3.0 s, what is the magnitude of its acceleration, assuming that it continues to move in a straight line?

Learn how to calculate the magnitude of acceleration when a car slows down from 80 mi/h to 50 mi/h in 3 seconds. This problem covers key concepts in kinematics, including linear motion, velocity change, and unit conversion. Suitable for students in Grades 9-12.

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