Kinematics Problem: Finding Particle Position

This problem involves calculating the final position of a particle undergoing constant acceleration. We use the standard kinematic equation for motion with constant acceleration.

Relevant Formula

The position ($S$) of a particle at time ($t$) is given by:

$S = S_0 + V_0 t + \frac{1}{2} a t^2$

Where:

• $S$ = final position
• $S_0$ = initial position
• $V_0$ = initial velocity
• $t$ = time
• $a$ = acceleration

Applying the Formula

We are given:

• Initial velocity, $V_0 = 12\ m/s$ (to the right, considered positive)
• Initial position, $S_0 = 0\ m$
• Time, $t = 10\ s$
• Acceleration, $a = -2\ m/s^2$ (to the left, considered negative)

Substitute these values into the equation:

$S = 0 + (12\ m/s)(10\ s) + \frac{1}{2} (-2\ m/s^2)(10\ s)^2$

Calculation Steps

1. Calculate the displacement due to initial velocity: $(12\ m/s)(10\ s) = 120\ m$.
2. Calculate the displacement due to acceleration: $\frac{1}{2} (-2\ m/s^2)(100\ s^2) = -100\ m$.
3. Add the displacements to the initial position: $S = 0 + 120\ m - 100\ m$.
4. Final Position: $S = 20\ m$.

The final position of the particle after 10 seconds is 20 meters.