A body of $5 ext{ kg}$ is moving with a velocity of $20 ext{ m/s}$. If a force of $100 ext{ N}$ is appli

Question

A body of $5 	ext{ kg}$ is moving with a velocity of $20 	ext{ m/s}$. If a force of $100 	ext{ N}$ is applied on it for $10 	ext{ sec}$ in the same direction as its velocity, what will now be the velocity of the body?

Accepted Answer

1. **Identify Given Data:** Mass $m = 5 	ext{ kg}$, initial velocity $u = 20 	ext{ m/s}$, Force $F = 100 	ext{ N}$, time $t = 10 	ext{ s}$.
2. **Method 1: Using Newton's Second Law and Kinematics**
   - Calculate acceleration using Newton's Second Law: $a = \frac{F}{m} = \frac{100}{5} = 20 	ext{ m/s}^2$ [Source 105, 126].
   - Use the first equation of motion: $v = u + at$ [Source 104].
   - $v = 20 + (20 	imes 10) = 20 + 200 = 220 	ext{ m/s}$.
3. **Method 2: Using Impulse-Momentum Theorem**
   - Impulse $J = F \Delta t = 100 	imes 10 = 1000 	ext{ N s}$.
   - Change in momentum $\Delta p = m(v - u)$.
   - $1000 = 5(v - 20) \implies 200 = v - 20 \implies v = 220 	ext{ m/s}$ [Source 131].

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