- Initial Velocity
The given problem states that a particle starts from a point with an initial velocity of 6 metre per second. This means that the particle is already in motion with a velocity of 6 m/s.
- Acceleration
The particle also has an acceleration of -20 m per second square. This means that the particle is decelerating or slowing down at a rate of 20 m/s^2.
- Using Kinematic Equations
To find out where the particle will be after 6 seconds, we can use the kinematic equations of motion. We can use the following equation:
d = vi*t + (1/2)*a*t^2
where d is the distance travelled, vi is the initial velocity, a is the acceleration, and t is the time elapsed.
Substituting the given values in the above equation, we get:
d = 6*6 + (1/2)*(-20)*(6^2)
On solving the above equation, we get:
d = -36 + 360
d = 324 m
- Conclusion
Therefore, we can conclude that after 6 seconds, the particle will be at a distance of 324 m from its starting point. However, the problem also states that the particle will be back at its starting point after 6 seconds. This means that the particle must have travelled a total distance of 0 m. Hence, the above calculation is incorrect.
- Reasoning
Since the particle starts and ends at the same point, the net displacement of the particle must be 0 m. This means that the particle would have travelled a total distance of 0 m in 6 seconds. Therefore, the particle must have come to a stop at some point and then reversed its direction, travelling back towards its starting point.
- Revised Calculation
To find out when the particle will come to a stop, we can use the following equation:
v = vi + a*t
where v is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time elapsed.
Substituting the given values in the above equation, we get:
0 = 6 + (-20)*t
On solving the above equation, we get:
t = 0.3 s
This means that the particle will come to a stop after 0.3 seconds. After this, the particle will reverse its direction and start moving back towards its starting point. Since the acceleration is constant, the particle will take the same amount of time to come to a stop as it did to start moving. Therefore, the particle will reach its starting point after