A spaceship is traveling at a velocity of when its rockets fire, giving it an acceleration of V = Vo = (37.9 m/s) i How fast, in meters per second, is the rocket moving 5.19 s after the rockets fire? m/s à = (2.52 m/s²) + (4.19 m/s²)ĵ
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.
![**Vector Velocity and Acceleration Problem**
*A spaceship is traveling at a velocity of:*
\[ \vec{v}_0 = (37.9 \, \text{m/s}) \, \hat{\imath} \]
*when its rockets fire, giving it an acceleration of:*
\[ \vec{a} = (2.52 \, \text{m/s}^2) \, \hat{\imath} + (4.19 \, \text{m/s}^2) \, \hat{\jmath} \]
**Problem:**
How fast, in meters per second, is the rocket moving \( 5.19 \, \text{s} \) after the rockets fire?
\[ v = \, \_\_\_\_\_\_\_\_\_\_ \, \text{m/s} \]
*Instructions for Solving:*
1. Use the equation for velocity:
\[ \vec{v} = \vec{v}_0 + \vec{a} \cdot t \]
2. Substitute the given values:
\[ \vec{v} = (37.9 \, \text{m/s}) \, \hat{\imath} + \left((2.52 \, \text{m/s}^2) \, \hat{\imath} + (4.19 \, \text{m/s}^2) \, \hat{\jmath}\right) \cdot 5.19 \, \text{s} \]
3. Calculate separately for each component.
4. Combine the final values to find the resultant velocity vector.
*Remember to fill in the solution in the space provided.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38a9992d-9c05-40da-9474-aaafff450dc4%2F5a2b2f59-c054-4b68-a96d-21e8af0659f1%2F54di0hn_processed.png&w=3840&q=75)
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