A sports car moving at constant speed travels 120 m
in 5.5 s
, then brakes and comes to a stop in 3.7 s
.What is the magnitude of its acceleration in  m/s2
?
Express your answer using two significant figures.

To solve for the magnitude of the car's acceleration, we need to find the rate at which its velocity changes as it comes to a stop.

### Step-by-Step Solution:

1. **Determine the initial velocity:**

   Since the car is moving at a constant speed before braking, we can calculate its initial velocity (\( v_i \)) using the distance traveled and the time taken:

   \[
   v_i = \frac{\text{distance}}{\text{time}} = \frac{120 \, \text{m}}{5.5 \, \text{s}}
   \]

2. **Calculate the initial velocity:**

   Let's compute \( v_i \):

   \[
   v_i = \frac{120}{5.5} \, \text{m/s}
   \]

3. **Determine the acceleration:**

   When the car brakes, it decelerates to a stop in 3.7 seconds. The final velocity (\( v_f \)) is 0 m/s, and the initial velocity is \( v_i \). The acceleration \( a \) can be calculated using the formula:

   \[
   a = \frac{v_f - v_i}{t}
   \]

   Since \( v_f = 0 \), this simplifies to:

   \[
   a = \frac{0 - v_i}{3.7}
   \]

   Substitute \( v_i \) to find \( a \).

### Calculation:

Now, let's perform the calculations.1. **Initial velocity (\(v_i\))**:  
   The car's initial velocity before braking is approximately \(21.82 \, \text{m/s}\).

2. **Magnitude of acceleration**:  
   The magnitude of the car's acceleration while braking is \(5.9 \, \text{m/s}^2\).

Would you like further details or have any questions?

### Related Questions:
1. What is the distance covered by the car while it is braking?
2. How much kinetic energy did the car have before it started braking?
3. What is the average velocity of the car during the braking period?
4. How would the acceleration change if the braking time was reduced by half?
5. What force is required to stop a car of mass 1000 kg with the calculated acceleration?

**Tip:** Remember that negative acceleration (deceleration) indicates a reduction in speed.

Learn how to calculate the magnitude of acceleration for a sports car that travels 120 meters in 5.5 seconds at constant speed and then brakes to a stop in 3.7 seconds. The solution involves using the acceleration formula and understanding kinematic concepts. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation