An object is moving east and its velocity changes from 65 m/s to 25 m/s in 10 seconds
The Correct Answer and Explanation is:
To calculate the acceleration of an object, use the formula:Acceleration (a)=Final velocity (v)−Initial velocity (u)Time (t)\text{Acceleration (a)} = \frac{\text{Final velocity (v)} – \text{Initial velocity (u)}}{\text{Time (t)}}Acceleration (a)=Time (t)Final velocity (v)−Initial velocity (u)
Given:
Initial velocity, u=65 m/su = 65 \, \text{m/s}u=65m/s
Final velocity, v=25 m/sv = 25 \, \text{m/s}v=25m/s
Time, t=10 st = 10 \, \text{s}t=10sa=25 m/s−65 m/s10 s=−40 m/s10 s=−4 m/s2a = \frac{25 \, \text{m/s} – 65 \, \text{m/s}}{10 \, \text{s}} = \frac{-40 \, \text{m/s}}{10 \, \text{s}} = -4 \, \text{m/s}^2a=10s25m/s−65m/s=10s−40m/s=−4m/s2
Answer: -4 m/s²
Explanation:
Acceleration is defined as the rate at which the velocity of an object changes over time. It can be either positive (when the object is speeding up) or negative (when the object is slowing down). In this scenario, the object is moving eastward and its velocity decreases from 65 m/s to 25 m/s over a time interval of 10 seconds. Since the velocity is decreasing, the object is experiencing negative acceleration, also called deceleration.
To compute the acceleration, subtract the initial velocity from the final velocity. In this case:
- Final velocity = 25 m/s
- Initial velocity = 65 m/s
- The change in velocity = 25−65=−40 m/s25 – 65 = -40 \, \text{m/s}25−65=−40m/s
Now divide the change in velocity by the time taken:Acceleration=−40 m/s10 s=−4 m/s2\text{Acceleration} = \frac{-40 \, \text{m/s}}{10 \, \text{s}} = -4 \, \text{m/s}^2Acceleration=10s−40m/s=−4m/s2
The negative sign indicates that the object is slowing down in the direction it was originally moving (east). This is a typical case of deceleration, which still counts as acceleration in physics, but the negative sign tells us the direction of change is opposite to the motion.
Therefore, the object’s acceleration is –4 meters per second squared.
