A poorly tuned Prius can accelerate from rest to a speed of 28 m/s in 20s.
a) what is the average acceleration of the car?
my answer is 1.4
b) Find its displacement in this time.
my answer = 280
Can anyone verify this please?
correct. good work.
Oh, I can verify it, but I'll do it in a clownish way, just for fun!
a) The average acceleration of the car is like when you start a car, hit the gas pedal, and then immediately step on the brake. It's confusing, really. So, to find the average acceleration, we take the change in velocity and divide it by the time it took. In this case, it would be (28 m/s - 0 m/s) / 20 s = 1.4 m/s². Ding, ding, we have a winner! Your answer is correct. You're on a roll!
b) Ah, the displacement of the Prius. It's like being on a road trip with no GPS and only relying on a compass. Okay, so to find the displacement, we need to multiply the average velocity by the time. In this case, the average velocity is (28 m/s + 0 m/s) / 2 = 14 m/s. So, the displacement would be 14 m/s x 20 s = 280 meters. Ta-da! You nailed it again!
So, congratulations on that mind-blowingly accurate calculations, my friend!
a) To find the average acceleration, you need to use the formula:
average acceleration = (final velocity - initial velocity) / time
Given that the initial velocity is 0 m/s, the final velocity is 28 m/s, and the time is 20 s, you can calculate the average acceleration as follows:
average acceleration = (28 m/s - 0 m/s) / 20 s = 28 m/s / 20 s = 1.4 m/s²
Therefore, your answer of 1.4 m/s² is correct.
b) To find the displacement, you can use the formula:
displacement = (initial velocity × time) + (0.5 × average acceleration × time²)
Given that the initial velocity is 0 m/s, the average acceleration is 1.4 m/s², and the time is 20 s, you can calculate the displacement as follows:
displacement = (0 m/s × 20 s) + (0.5 × 1.4 m/s² × (20 s)²)
displacement = 0 m + (0.5 × 1.4 m/s² × 400 s²)
displacement = 0 m + 280 m = 280 m
Therefore, your answer of 280 m is also correct.
To verify your answers, let's go through the calculations step by step.
a) To find the average acceleration, we need to use the formula:
Average Acceleration = (Final Velocity - Initial Velocity) / Time
Given:
Initial Velocity (u) = 0 m/s (since it starts from rest)
Final Velocity (v) = 28 m/s
Time (t) = 20 s
Plugging in the values:
Average Acceleration = (28 m/s - 0 m/s) / 20 s
= 28 m/s / 20 s
= 1.4 m/s²
So, your answer of 1.4 m/s² for the average acceleration is correct.
b) To find the displacement, we can use the formula:
Displacement = (Initial Velocity + Final Velocity) / 2 * Time
Given:
Initial Velocity (u) = 0 m/s (since it starts from rest)
Final Velocity (v) = 28 m/s
Time (t) = 20 s
Plugging in the values:
Displacement = (0 m/s + 28 m/s) / 2 * 20 s
= 14 m/s * 20 s
= 280 m
So, your answer of 280 m for the displacement is also correct.
Therefore, your answers for both parts (a) and (b) are correct.