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A Ferrari moves with rectilinear motion. The speed increases from zero to 60mi/hr in 3.5sec, then decreases to zero in 2sec.

Calculate:
Acceleration during the first 3.5sec and during the next 2sec (m/s2)
The distance travelled in the 5.5sec (m)
How long does the car need to go to 50m (sec)

User Bitcell
by
7.7k points

1 Answer

1 vote

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.

User The E
by
8.7k points
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