An object moves in one dimensional motion with constant acceleration a = 3.4 m/s2.  At time t = 0 s, the object is at x0 = 1.6 m and has an initial velocity of v0 = 2.9 m/s.

How far will the object move before it achieves a velocity of v = 7.8 m/s?

Your answer should be accurate to the nearest 0.1 m.

We can solve this problem using the kinematic equation that relates velocity, acceleration, and displacement:

\[
v^2 = v_0^2 + 2a(x - x_0)
\]

Where:
- \(v\) is the final velocity (7.8 m/s),
- \(v_0\) is the initial velocity (2.9 m/s),
- \(a\) is the acceleration (3.4 m/s²),
- \(x_0\) is the initial position (1.6 m),
- \(x\) is the final position.

We need to solve for the displacement, \( \Delta x = x - x_0 \).

### Rearranging the equation for \(x - x_0\):
\[
v^2 = v_0^2 + 2a(x - x_0)
\]
\[
x - x_0 = \frac{v^2 - v_0^2}{2a}
\]

Now, plug in the values:
\[
x - x_0 = \frac{(7.8)^2 - (2.9)^2}{2(3.4)}
\]

Let's calculate this.The displacement of the object before it reaches a velocity of 7.8 m/s is approximately 7.7 meters. Therefore, the object will move **7.7 meters** from its initial position.

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

Here are 5 related questions to expand on this:
1. How long does it take for the object to reach a velocity of 7.8 m/s?
2. What is the total distance traveled after 5 seconds?
3. If the acceleration was negative, how would the displacement change?
4. How would the problem change if the object started at rest?
5. What would be the displacement if the final velocity was doubled?

**Tip:** In problems with constant acceleration, the kinematic equations are invaluable for relating displacement, velocity, time, and acceleration.

An object moves in one dimensional motion with constant acceleration a = 3.4 m/s². At time t = 0 s, the object is at x₀ = 1.6 m and has an initial velocity of v₀ = 2.9 m/s. How far will the object move before it achieves a velocity of v = 7.8 m/s? Your answer should be accurate to the nearest 0.1 m.

Learn how to solve a kinematic problem where an object moves with constant acceleration. The problem involves calculating the displacement before the object reaches a specified velocity. Key concepts include kinematic equations and linear motion, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation