Answer: approx 3.61 seconds
Step-by-step explanation:
To calculate the acceleration during the first 3.5 seconds and the next 2 seconds, we can use the formula:
Acceleration = Change in Velocity / Time
First, let's convert the speed from miles per hour to meters per second:
60 mi/hr = (60 * 1609.34 m) / (1 hr * 3600 sec) ≈ 26.82 m/s
Acceleration during the first 3.5 seconds:
Velocity change = 26.82 m/s - 0 m/s = 26.82 m/s
Time = 3.5 sec
Acceleration = 26.82 m/s / 3.5 sec ≈ 7.66 m/s²
Acceleration during the next 2 seconds:
Velocity change = 0 m/s - 26.82 m/s = -26.82 m/s (negative sign indicates deceleration)
Time = 2 sec
Acceleration = -26.82 m/s / 2 sec ≈ -13.41 m/s²
To calculate the distance traveled in the 5.5 seconds, we can use the formula:
Distance = Initial Velocity * Time + (1/2) * Acceleration * Time²
For the first part (acceleration):
Initial Velocity = 0 m/s
Time = 3.5 sec
Acceleration = 7.66 m/s²
Distance = 0 m/s * 3.5 sec + (1/2) * 7.66 m/s² * (3.5 sec)² ≈ 44.89 meters
For the second part (deceleration):
Initial Velocity = 26.82 m/s (velocity at the end of the first part)
Time = 2 sec
Acceleration = -13.41 m/s²
Distance = 26.82 m/s * 2 sec + (1/2) * (-13.41 m/s²) * (2 sec)² ≈ 20.93 meters
Total distance traveled in 5.5 seconds:
Total Distance = Distance during acceleration + Distance during deceleration
Total Distance = 44.89 meters + 20.93 meters ≈ 65.82 meters
To calculate how long the car needs to go 50 meters, we can use the formula:
Distance = Initial Velocity * Time + (1/2) * Acceleration * Time²
For the first part (acceleration):
Initial Velocity = 0 m/s
Distance = 50 meters
Acceleration = 7.66 m/s²
50 meters = 0 m/s * Time + (1/2) * 7.66 m/s² * Time²
Simplifying the equation:
3.83 m/s² * Time² = 50 meters
Time² = 50 meters / 3.83 m/s²
Taking the square root of both sides:
Time ≈ √(50 meters / 3.83 m/s²)
Time ≈ √(13.05 seconds²) ≈ 3.61 seconds
Therefore, the car needs approximately 3.61 seconds to travel 50 meters.