Final answer:
The displacement of Ben's car during the time period is 201.72 meters. Ben's car, accelerating from rest to 24 m/s in 4.10 seconds, achieves a displacement of approximately 49.14 meters during this time period.
Step-by-step explanation:
To calculate the displacement of Ben's car during the time period, we can use the equation:
displacement = (initial velocity * time) + (0.5 * acceleration * time^2)
Given that the initial velocity is 0 m/s, the final velocity is 24 m/s, and the time is 4.10 seconds, we can substitute these values into the equation:
displacement = (0 * 4.10) + (0.5 * 24 * 4.10^2)
Simplifying the equation, we get:
displacement = 0 + (0.5 * 24 * 16.81)
displacement = 0 + 201.72
displacement = 201.72 meters
Ben's car, accelerating from rest to 24 m/s in 4.10 seconds, achieves a displacement of approximately 49.14 meters during this time period.
To determine the displacement of Ben's car during the acceleration, we can use the formula for displacement under constant acceleration from rest, which is ½at² where ‘a’ is the acceleration and ‘t’ is the time. Given that Ben's car accelerates from rest to 24 m/s in a time of 4.10 seconds, we first need to calculate the acceleration.
The acceleration ‘a’ can be found using the formula a = Δv/Δt, where Δv is the change in velocity and Δt is the change in time. Ben's velocity change Δv is 24 m/s (from rest) in a time Δt of 4.10 s. So the acceleration is a = 24 m/s / 4.10 s = 5.85 m/s².
Now, the displacement 'd' can be determined by substituting the values into the formula ½at²:
d = ½(5.85 m/s²)(4.10 s)² = ½(5.85 m/s²)(16.81 s²) = ½(98.2855 m) = 49.14275 m. Therefore, Ben's car has a displacement of approximately 49.14 meters during the 4.10 seconds of acceleration.