An object travels 60m in the first 6sec. Then keeps uniform motion for the next 9sec. In the last 10sec of the journey it decelerates uniformly to rest. Find the maximum speed attained in the journey. Find the total distance traveled in the whole journey.?

Question

Answer

Total distance=60+90+85=235m..I think maximum speed=10m/s

Answer

Analysis of the Journey:
- First 6 seconds: The object travels 60m in the first 6 seconds.
- Next 9 seconds: The object maintains uniform motion for the next 9 seconds.
- Last 10 seconds: The object decelerates uniformly to rest in the last 10 seconds.

Finding the Maximum Speed:
- First, calculate the speed of the object during the first 6 seconds using the formula:
Speed = Distance / Time
Speed = 60m / 6s = 10 m/s
- Next, calculate the acceleration during deceleration in the last 10 seconds using the formula:
Acceleration = Change in Velocity / Time
Acceleration = (0 - 10) m/s / 10s = -1 m/s^2
- Using the formula for uniformly decelerating motion:
Final Velocity = Initial Velocity + (Acceleration * Time)
Final Velocity = 10 m/s + (-1 m/s^2 * 10s) = 0 m/s
- Therefore, the maximum speed attained during the journey is 10 m/s.

Finding the Total Distance:
- Calculate the distance covered during uniform motion for the next 9 seconds:
Distance = Speed * Time
Distance = 10 m/s * 9s = 90m
- Calculate the distance covered during deceleration in the last 10 seconds:
Distance = Initial Velocity * Time + 0.5 * Acceleration * Time^2
Distance = 10 m/s * 10s + 0.5 * (-1 m/s^2) * (10s)^2 = 50m
- Therefore, the total distance traveled in the whole journey is:
60m + 90m + 50m = 200m.

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