Question

An object travels north with a velocity of $ 10\text{ }m{{s}^{-1}} $ and then speeds up to a velocity of $ 25\text{ }m{{s}^{-1}} $ in 5 s. The acceleration of the object in these 5 s is:

• A. $ 3\text{ }m{{s}^{-1}} $ in north direction
• B. \(3\text{ }m{{s}^{-2}}\) in north direction
• C. $ \text{15 }m{{s}^{-2}} $ in north direction
• D. $ \text{3 }m{{s}^{-2}} $ in south direction

Answer 1

The Correct Option is B

The correct option is(B): \(3\text{ }m{{s}^{-2}}\)in north direction.

\(a=\frac{v-u}{t}=\frac{25-10}{5}\) \(=\frac{15}{5}=3\,m/{{s}^{2}}\) in north direction.

Answer 2

To find the acceleration of the object, we use the formula for acceleration, which is the change in velocity divided by the time over which the change occurs. The formula is:

\[ a = \frac{\Delta v}{\Delta t} \]

Given:
- Initial velocity (\( v_0 \)) = \( 10 \, \text{m/s} \)
- Final velocity (\( v_f \)) = \( 25 \, \text{m/s} \)
- Time interval (\( \Delta t \)) = \( 5 \, \text{s} \)

First, we calculate the change in velocity (\( \Delta v \)):

\[ \Delta v = v_f - v_0 \]
\[ \Delta v = 25 \, \text{m/s} - 10 \, \text{m/s} \]
\[ \Delta v = 15 \, \text{m/s} \]

Now, we use the change in velocity and the time interval to find the acceleration:

\[ a = \frac{15 \, \text{m/s}}{5 \, \text{s}} \]
\[ a = 3 \, \text{m/s}^2 \]

Therefore, the acceleration of the object over these 5 seconds is \( 3 \, \text{m/s}^2 \).
Thus the correct answer is Option B \(3\frac{m}{s^2} \) in North direction