A particle of mass 50 g travels along a straight line. The...

The mass of the particle is given as $m = 50 \text{ g} = 0.05 \text{ kg}$.

The acceleration $a$ of the particle is the slope of the velocity-time graph, and the force is given by Newton's second law, $F = ma$.

At $t = 2 \text{ s}$, the particle is in the time interval $0$ to $3 \text{ s}$. The slope of the $v-t$ graph is:
$a = \dfrac{15 - 0}{3 - 0} = 5 \text{ m/s}^2$
The force is $F = 0.05 \times 5 = 0.25 \text{ N}$. Since the acceleration is positive, the force is along the direction of motion.

At $t = 4 \text{ s}$, the particle is in the time interval $3$ to $5 \text{ s}$. The velocity is constant, so the slope is zero:
$a = 0$
The force is $F = 0.05 \times 0 = 0 \text{ N}$.

At $t = 6 \text{ s}$, the particle is in the time interval $5$ to $8 \text{ s}$. The slope of the $v-t$ graph is:
$a = \dfrac{0 - 15}{8 - 5} = -5 \text{ m/s}^2$
The force is $F = 0.05 \times (-5) = -0.25 \text{ N}$. The negative sign indicates that the force is acting opposite to the direction of motion.