A car accelerates uniformly from rest to a
speed of 23.9 km/h in 8.2 s.
Find the distance it travels during this time.
Answer in units of m
Why did the car bring a map on its acceleration journey? Because it wanted to calculate the distance traveled!
To find the distance traveled, we can use the equation:
distance = (initial velocity)(time) + (1/2)(acceleration)(time^2)
Given that the initial velocity is 0 km/h and the time is 8.2 s, we can convert the initial velocity to m/s by multiplying it by 1000/3600 (because 1 km/h = 1000 m/3600 s).
So, the initial velocity is 0 m/s, and the time is 8.2 s. Now, let's calculate the distance traveled! *drumroll*
distance = (0 m/s)(8.2 s) + (1/2)(acceleration)(8.2 s)^2
Since the car is accelerating uniformly, we don't know the value of acceleration. But guess what? It's irrelevant in this calculation. Why? Because the car only accelerated, which means there was no change in velocity to account for. So, the distance traveled will be zero! Just kidding!
Hence, the distance traveled by the car during this time is 0 meters. Now, doesn't that bring a smile to your face?
To find the distance traveled by the car, we can use the formula:
\[ d = \frac{1}{2} \cdot a \cdot t^2 \]
Where:
d = distance traveled
a = acceleration
t = time
We are given that the car accelerates uniformly from rest to a speed of 23.9 km/h in 8.2 s. We first need to convert the speed from km/h to m/s. Since 1 km = 1000 m and 1 h = 3600 s:
23.9 km/h × (1000 m/1 km) × (1 h/3600 s) = 6.64 m/s
Now we can plug the values into the formula:
\[ d = \frac{1}{2} \cdot 6.64 \, \text{m/s} \cdot (8.2 \, \text{s})^2 \]
Simplifying:
\[ d = \frac{1}{2} \cdot 6.64 \, \text{m/s} \cdot 67.24 \, \text{s}^2 \]
\[ d = 224.83 \, \text{m} \]
Therefore, the car travels a distance of approximately 224.83 meters during this time.
To find the distance traveled by the car during this time, we can use the equation for uniformly accelerated motion:
\[d = \frac{1}{2}at^2\]
Where:
d is the distance traveled,
a is the acceleration, and
t is the time taken.
In this case, the car starts from rest, so its initial velocity (u) is zero. The final velocity (v) is given as 23.9 km/h, and the time taken (t) is 8.2 seconds.
First, let's convert the final velocity from km/h to m/s. We know that 1 km/h is equal to 1000/3600 m/s.
Speed in m/s = 23.9 km/h * (1000/3600) = 6.64 m/s (rounded to two decimal places)
Next, we can calculate the acceleration (a). Since the car is starting from rest (u=0), we can use the formula:
\[a = \frac{v - u}{t} = \frac{6.64 - 0}{8.2}\]
a = 0.81 m/s^2 (rounded to two decimal places)
Finally, substitute the values of a and t into the equation for distance (d):
\[d = \frac{1}{2}at^2 = \frac{1}{2} * 0.81 * (8.2)^2\]
d ≈ 26.70 meters (rounded to two decimal places)
Therefore, the distance traveled by the car during this time is approximately 26.70 meters.