A jet plane lands with a speed of 100 m/s and can accelerate at a maximum rate of -5.00 m/s2
as it comes to rest.
(a) From the instant the plane touches the runway, what is the minimum time needed
before it can come to rest?

To solve this problem, we can use the kinematic equation that relates initial velocity, acceleration, and time. The relevant equation is:

\[
v_f = v_i + at
\]

where:
- \( v_f \) is the final velocity (0 m/s, since the plane comes to rest).
- \( v_i \) is the initial velocity (100 m/s).
- \( a \) is the acceleration (-5.00 m/s², negative because it is decelerating).
- \( t \) is the time, which we need to find.

Plugging in the known values:

\[
0 = 100 + (-5)t
\]

Solving for \( t \):

\[
0 = 100 - 5t \\
5t = 100 \\
t = \frac{100}{5} \\
t = 20 \, \text{s}
\]

So, the minimum time needed for the jet plane to come to rest is **20 seconds**.

Would you like further details or have any questions? Here are some related questions:

1. What is the minimum distance required for the plane to come to rest?
2. How would the time change if the plane's initial speed were different?
3. What is the significance of the negative sign in acceleration?
4. How would you find the plane's velocity at any given time during its deceleration?
5. How does changing the acceleration rate affect the stopping time?

**Tip:** Always keep track of the signs of velocity and acceleration when solving kinematics problems to ensure consistency with the direction of motion.

Discover the minimum time required for a jet plane, landing at 100 m/s, to decelerate to rest using kinematic equations. Solve for time with a detailed step-by-step explanation. Ideal for high school physics 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