https://file.aiquickdraw.com/mathbot/file/1727551426349i6e1mn84.jpg

We are given the following problem:

- Initial speed of the car, \( v_0 = 70 \, \text{km/h} = \frac{70 \times 1000}{3600} \, \text{m/s} \).
- Retardation (negative acceleration), \( a = 5 \, \text{m/s}^2 \).
- Distance to the obstacle, \( d = 60 \, \text{m} \).

We need to determine if the car comes to rest before hitting the obstacle and, if so, by how much distance.

### Formula to use:
We can use the equation of motion:
\[
v^2 = v_0^2 + 2 a d
\]
where:
- \( v \) is the final velocity (which should be 0 when the car comes to rest),
- \( v_0 \) is the initial velocity,
- \( a \) is the retardation (acceleration in the negative direction),
- \( d \) is the stopping distance.

Let me calculate the required stopping distance and check if it is less than or greater than 60 meters.The stopping distance for the car is approximately \( 37.81 \, \text{m} \).

Since the car comes to rest after traveling 37.81 meters, which is less than the 60 meters distance to the obstacle, the car stops safely before reaching the obstacle. The remaining distance before hitting the obstacle is:

\[
60 \, \text{m} - 37.81 \, \text{m} = 22.19 \, \text{m}.
\]

So, the car comes to rest with a remaining distance of about 22.19 meters before the obstacle.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the stopping distance change if the retardation were less, say 3 m/s²?
2. What if the initial speed were higher, for example, 90 km/h?
3. How does the reaction time of the driver factor into real-world braking distances?
4. How can wet or icy road conditions affect the retardation and stopping distance?
5. What equations are used to calculate the time taken to stop?

**Tip:** Always ensure to convert all units (e.g., km/h to m/s) before performing calculations in physics problems.

A driver is keeping to a steady 70 km/h when he sees that 60 m ahead the road is blocked because of an accident. He immediately applies his brakes to produce a retardation of 5 m/s². Does he come to rest before the accident and if so by how much?

Solve the kinematics problem involving a driver moving at 70 km/h who applies brakes with a retardation of 5 m/s². Determine if the car comes to rest before hitting a roadblock 60 meters ahead and calculate the remaining distance.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation