A particle of mass 1 g moves on a straight line. The variation of its velocity with time is shown in fig. Find the force acting on the particle att = 1 s,4s and 7 s.

Explanation

To solve the problem, we need to determine the force acting on a particle of mass 1 g (which is 0.001 kg) at three different times: t = 1 s, t = 4 s, and t = 7 s. The force can be calculated using Newton's second law, \( F = ma \), where \( a \) is the acceleration of the particle.

### Step 1: Find the acceleration at t = 1 s
- From the velocity-time graph, we can determine the acceleration by finding the slope of the line between t = 0 s and t = 3 s.
- The initial velocity \( v_i = 0 \) m/s (at t = 0 s) and the final velocity \( v_f = 15 \) m/s (at t = 3 s).
- The time interval \( \Delta t = 3 - 0 = 3 \) s.

Using the formula for acceleration:
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