Question

A body of mass \(2\) kg is moving with a velocity of \(10\,\text{m s}^{-1}\). If a force of \(50\) N is applied on it for \(10\) s along its motion, the velocity of the body (in \(\text{m s}^{-1}\)) is

• A. \(220\)
• B. \(200\)
• C. \(150\)
• D. \(175\)
• E. \(260\)

Hint:

Always use \(F=ma\) to find acceleration, then apply kinematic equations like \(v=u+at\) when time is given.

Answer 1

Answer: (E)

Step 1: Write the given data.
Mass of the body: \[ m=2\,\text{kg} \] Initial velocity: \[ u=10\,\text{m s}^{-1} \] Force applied: \[ F=50\,\text{N} \] Time: \[ t=10\,\text{s} \]

Step 2: Find the acceleration using Newton's second law.
\[ F=ma \Rightarrow a=\frac{F}{m}=\frac{50}{2}=25\,\text{m s}^{-2} \]

Step 3: Use the equation of motion.
We use: \[ v=u+at \]

Step 4: Substitute the values.
\[ v=10+25\times 10 \]

Step 5: Simplify.
\[ v=10+250=260\,\text{m s}^{-1} \]

Step 6: Interpret the result.
The velocity increases because the force is applied in the direction of motion.

Step 7: State the final answer.
Thus, the final velocity is:
\[ \boxed{260\,\text{m s}^{-1}} \] which matches option \((5)\).