If the velocity of an object changes from 65 m/s to 98 M/s during a time interval of 12 s what is the acceleration of the object
The Correct Answer and Explanation is:
Answer:
To find the acceleration, we use the formula:Acceleration=Final velocity−Initial velocityTime\text{Acceleration} = \frac{{\text{Final velocity} – \text{Initial velocity}}}{{\text{Time}}}Acceleration=TimeFinal velocity−Initial velocity
Given:
- Initial velocity (viv_ivi) = 65 m/s
- Final velocity (vfv_fvf) = 98 m/s
- Time (ttt) = 12 seconds
a=98 m/s−65 m/s12 s=33 m/s12 s=2.75 m/s2a = \frac{{98\, \text{m/s} – 65\, \text{m/s}}}{{12\, \text{s}}} = \frac{{33\, \text{m/s}}}{{12\, \text{s}}} = 2.75\, \text{m/s}^2a=12s98m/s−65m/s=12s33m/s=2.75m/s2
Correct Answer: 2.75 m/s²
Textbook-style Explanation
Acceleration is a measure of how quickly the velocity of an object changes with time. In physics, it is defined as the change in velocity divided by the time taken for that change. It is a vector quantity, meaning it has both magnitude and direction. When an object speeds up, its acceleration is positive. When it slows down, its acceleration is negative (also called deceleration).
To calculate the acceleration, the following formula is used:a=vf−vita = \frac{{v_f – v_i}}{t}a=tvf−vi
where:
- aaa is the acceleration,
- vfv_fvf is the final velocity,
- viv_ivi is the initial velocity,
- ttt is the time interval.
In this problem, the object starts with an initial velocity of 65 m/s and increases its speed to 98 m/s over a time period of 12 seconds. Substituting these values into the formula:a=98 m/s−65 m/s12 s=33 m/s12 s=2.75 m/s2a = \frac{{98\, \text{m/s} – 65\, \text{m/s}}}{12\, \text{s}} = \frac{33\, \text{m/s}}{12\, \text{s}} = 2.75\, \text{m/s}^2a=12s98m/s−65m/s=12s33m/s=2.75m/s2
This result means that the object’s velocity is increasing by 2.75 meters per second every second. In real-world terms, if this object were a car, its speed would be increasing smoothly by that rate throughout the 12-second period.
Understanding acceleration is crucial in many areas of science and engineering, from analyzing motion in physics to designing safe transportation systems.
