A model rocket flies straight upward with constant acceleration, undergoing a displacement of 15.0 m during its first 0.25 s of travel. What was its speed at the end of the first 0.25 s, assuming it started from rest?
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
![**Question 10**
A model rocket flies straight upward with constant acceleration, undergoing a displacement of 15.0 m during its first 0.25 s of travel. What was its speed at the end of the first 0.25 s, assuming it started from rest?
*Explanation:*
Given that the rocket starts from rest, we can use the kinematic equation:
\[ s = ut + \frac{1}{2}at^2 \]
Where:
- \( s = 15.0 \, \text{m} \) (displacement)
- \( u = 0 \, \text{m/s} \) (initial velocity)
- \( t = 0.25 \, \text{s} \) (time)
- \( a \) is the acceleration
- \( v = u + at \) is the final velocity.
First, solve for acceleration \( a \):
\[ 15.0 = 0 \cdot 0.25 + \frac{1}{2}a(0.25)^2 \]
\[ 15.0 = \frac{1}{2}a(0.0625) \]
\[ 15.0 = 0.03125a \]
\[ a = \frac{15.0}{0.03125} \]
\[ a = 480 \, \text{m/s}^2 \]
Now, solve for the final velocity \( v \):
\[ v = 0 + (480)(0.25) \]
\[ v = 120 \, \text{m/s} \]
Therefore, the speed of the rocket at the end of the first 0.25 seconds is 120 m/s.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffd53d82-b6a8-4210-805b-6a3c6ec01562%2F10e17350-fe37-43b4-8973-76c6274220a2%2F31wx3bf_processed.jpeg&w=3840&q=75)
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