An object with a mass 10 kg moves at a constant velocity of $10 ext{ m/s}$. A constant force then acts for 4

Question

An object with a mass 10 kg moves at a constant velocity of $10 	ext{ m/s}$. A constant force then acts for 4 seconds on the object and gives it a speed of $2 	ext{ m/s}$ in the opposite direction. The acceleration produced in it is:

Accepted Answer

1. **Sign Convention:** Let the initial direction of motion be positive. 
   - Initial velocity, $u = +10 	ext{ m/s}$.
   - Final velocity, $v = -2 	ext{ m/s}$ (since it is in the opposite direction).
2. **Time:** The time interval, $t = 4 	ext{ s}$.
3. **Formula:** Acceleration ($a$) is defined as the rate of change of velocity.
   $$ a = \frac{v - u}{t} $$
   [Source 34]
4. **Calculation:**
   $$ a = \frac{-2 - 10}{4} $$
   $$ a = \frac{-12}{4} $$
   $$ a = -3 	ext{ m/s}^2 $$
   The negative sign indicates that the acceleration is acting in the direction opposite to the initial motion (retardation followed by acceleration in the reverse direction).

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