A race car traveling at 44 m/s is accelerated to a velocity of 22 m/s over an 11 s interval. What is the displacement of this time? (Could you show how you got the answer?) Thank you
Actually the car is decelerating. The average velocity during the interval is (22 + 44)/2 = 33 m/s.
Multiply that by 11 s for the distance covered. Looks like 363 m.
To find the displacement of the race car, we can use the formula for average velocity:
Average Velocity = Displacement / Time
Rearranging the formula, we have:
Displacement = Average Velocity * Time
Given that the initial velocity (u) is 44 m/s, the final velocity (v) is 22 m/s, and the time interval (t) is 11 s, we can calculate the average velocity as:
Average Velocity = (u + v) / 2
Substituting the given values:
Average Velocity = (44 m/s + 22 m/s) / 2 = 66 m/s / 2 = 33 m/s
Next, we substitute the average velocity and time into the displacement formula:
Displacement = Average Velocity * Time
Displacement = 33 m/s * 11 s
Displacement = 363 m
Therefore, the displacement of the race car over the 11 s interval is 363 meters.
To find the displacement of the race car, we can use the equation:
Displacement = Initial Velocity × Time + 0.5 × Acceleration × Time²
Given values:
Initial Velocity (u) = 44 m/s
Final Velocity (v) = 22 m/s
Time (t) = 11 s
We need to find the acceleration (a) first. We can use the equation:
Acceleration = (Final Velocity - Initial Velocity) / Time
Substituting the values:
Acceleration = (22 - 44) m/s / 11 s
Simplifying the equation:
Acceleration = -22 m/s / 11 s
Acceleration = -2 m/s²
Now we can substitute the values of initial velocity, time, and acceleration into the displacement equation:
Displacement = 44 m/s × 11 s + 0.5 × (-2 m/s²) × (11 s)²
Simplifying each term:
Displacement = 484 m + 0.5 × (-2 m/s²) × 121 s²
Displacement = 484 m - 1 m/s² × 121 s²
Displacement = 484 m - 121 m/s² × s²
Displacement = 484 m - 121 m × s²
So, the displacement of the race car over the 11 seconds interval is 363 meters.