A particle oscillates between the points x=40mm and x=160mm with an acceleration a =k(100-x),where k is a constant.The velocity of the particle is 8 m m/s when =100 mm and is zero at both x=40 mm and x=160mm.Determine (a)the value of k (b) the velocity when x=120 mm.

Explanation

To solve the problem, we need to determine the value of the constant \( k \) and the velocity of the particle when it is at \( x = 120 \, \text{mm} \).

### Step-by-step Solution:

1. **Understanding the Given Information**:
- The particle oscillates between \( x = 40 \, \text{mm} \) and \( x = 160 \, \text{mm} \).
- The acceleration is given by \( a = k(100 - x) \).
- The velocity is \( 8 \, \text{mm/s} \) when \( x = 100 \, \text{mm} \).
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