A vehicle with an initial speed of 70km/h, accelerates at 6000 km/h^2 on a straight pavement. How long will the car drive to end up with a speed of 120 km/h? What is the distance that the car travels within the timeframe?

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**Physics Problem on Motion with Constant Acceleration**

**Problem Statement:**

A vehicle with an initial speed of 70 km/h accelerates at 6000 km/h^2 on a straight pavement. How long will the car drive to end up with a speed of 120 km/h? What is the distance that the car travels within the timeframe?

**Solution:**

To solve this problem, we will use the equations of motion with constant acceleration.

Given Data:
- Initial speed (u): 70 km/h
- Final speed (v): 120 km/h
- Acceleration (a): 6000 km/h^2

1. **Time Calculation:**

Using the first equation of motion:
\[ v = u + at \]
Rearrange to solve for time (t):
\[ t = \frac{v - u}{a} \]

Substitute the given values:
\[ t = \frac{120 \ \text{km/h} - 70 \ \text{km/h}}{6000 \ \text{km/h}^2} \]
\[ t = \frac{50 \ \text{km/h}}{6000 \ \text{km/h}^2} \]
\[ t \approx 0.00833 \ \text{h} \]

Convert hours to seconds:
\[ t \approx 0.00833 \ \text{h} \times 3600 \ \text{s/h} \]
\[ t \approx 30 \ \text{s} \]

2. **Distance Calculation:**

Using the second equation of motion:
\[ s = ut + \frac{1}{2}at^2 \]

Substitute the given values:
\[ s = 70 \ \text{km/h} \times 0.00833 \ \text{h} + \frac{1}{2} \times 6000 \ \text{km/h}^2 \times (0.00833 \ \text{h})^2 \]
\[ s = 0.583 + \frac{1}{2} \times 6000 \times 0.0000694 \]
\[ s = 0.583 + 0.208 \]
\[ s \approx 0.791 \ \text{km} \]

**Summary:**

- The car will take approximately 30 seconds to reach a speed of 120 km/h.
- During this
Transcribed Image Text:**Physics Problem on Motion with Constant Acceleration** **Problem Statement:** A vehicle with an initial speed of 70 km/h accelerates at 6000 km/h^2 on a straight pavement. How long will the car drive to end up with a speed of 120 km/h? What is the distance that the car travels within the timeframe? **Solution:** To solve this problem, we will use the equations of motion with constant acceleration. Given Data: - Initial speed (u): 70 km/h - Final speed (v): 120 km/h - Acceleration (a): 6000 km/h^2 1. **Time Calculation:** Using the first equation of motion: \[ v = u + at \] Rearrange to solve for time (t): \[ t = \frac{v - u}{a} \] Substitute the given values: \[ t = \frac{120 \ \text{km/h} - 70 \ \text{km/h}}{6000 \ \text{km/h}^2} \] \[ t = \frac{50 \ \text{km/h}}{6000 \ \text{km/h}^2} \] \[ t \approx 0.00833 \ \text{h} \] Convert hours to seconds: \[ t \approx 0.00833 \ \text{h} \times 3600 \ \text{s/h} \] \[ t \approx 30 \ \text{s} \] 2. **Distance Calculation:** Using the second equation of motion: \[ s = ut + \frac{1}{2}at^2 \] Substitute the given values: \[ s = 70 \ \text{km/h} \times 0.00833 \ \text{h} + \frac{1}{2} \times 6000 \ \text{km/h}^2 \times (0.00833 \ \text{h})^2 \] \[ s = 0.583 + \frac{1}{2} \times 6000 \times 0.0000694 \] \[ s = 0.583 + 0.208 \] \[ s \approx 0.791 \ \text{km} \] **Summary:** - The car will take approximately 30 seconds to reach a speed of 120 km/h. - During this
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