Final answer:
To solve the problem, we first converted the Ferrari's initial and final velocities from km/h to m/s, then used the kinematic equations to calculate the acceleration, which is approximately 7.78 m/s². Finally, we calculated the distance covered as approximately 260.86 meters.
Step-by-step explanation:
To find the distance covered by the Ferrari, and calculate its acceleration, we can use the kinematic equations of motion. Given that the initial velocity (v0) is 20 km/h, the final velocity (v) is 230 km/h, and the time (t) is 7.5 seconds, we need to first convert velocities to meters per second (m/s) because the unit for acceleration is m/s2.
Converting km/h to m/s:
- v0 = 20 km/h × (1000 m/1 km) × (1 h/3600 s) = 5.56 m/s
- v = 230 km/h × (1000 m/1 km) × (1 h/3600 s) = 63.89 m/s
Acceleration (a) can be found using the formula:
a = (v - v0) / t
Calculating the acceleration:
a = (63.89 m/s - 5.56 m/s) / 7.5 s = 7.78 m/s2
To determine the distance (s), we can use the formula:
s = v0t + 0.5at2
Calculating the distance covered:
s = (5.56 m/s × 7.5 s) + 0.5 × 7.78 m/s2 × (7.5 s)2 = 41.7 m + 219.16 m = 260.86 m
The distance covered by the Ferrari during its acceleration is approximately 260.86 meters.