The maker of an automobile advertises that it takes 15 seconds to accelerate from 15 kilometers per hour to 70 kilometers per hour. Assuming constant acceleration,
(a) The distance the car travels during the 15 seconds (Round your answer to two decimal places.)
a = (70-15)/15 = 11/3 km/hr/s
Convert that to m/s^2, and then use
s(t) = 15km/hr * 15s + 11/6 km/hr/s * 15s^2
= 15km/hr * 15/3600 hr + 11/6 km/hr/s * 15s * 15/3600 hr
= 225/3600 + 11/6 * 225/3600 km
= 17/96 km
or 177 m
Don't like mixing up all those units?
15km/hr = 4.167 m/s
70km/hr = 19.444 m/s
So, a = (19.444-4.167)/15 = 1.018 m/s^2
s(t) = 4.167t + 0.509t^2
= 4.167*15 + 0.509*225
= 177m
To find the distance the car travels during the 15 seconds, we can use the formula:
Distance = Initial velocity * Time + (1/2) * Acceleration * Time^2
Given:
Initial velocity (u) = 15 km/h
Final velocity (v) = 70 km/h
Time (t) = 15 seconds
Since the question assumes constant acceleration, we need to find the acceleration first.
To find the acceleration, we can use the formula:
Acceleration = (Final velocity - Initial velocity) / Time
Let's calculate it:
Acceleration = (70 - 15) km/h / 15 seconds
Acceleration = 55 km/h / 15 seconds
Now, let's convert the acceleration from km/h to m/s:
Acceleration = 55 km/h * (1/3.6) m/s
Acceleration = 15.28 m/s
Now, let's calculate the distance:
Distance = Initial velocity * Time + (1/2) * Acceleration * Time^2
Distance = 15 km/h * (1/3.6) m/s * 15 s + (1/2) * 15.28 m/s * (15 s)^2
Distance = (15 * (15/3.6) + 0.5 * 15.28 * 15^2) m
Distance = 83.33 + 1725 m
Distance ≈ 1808.33 m
Therefore, the distance the car travels during the 15 seconds is approximately 1808.33 meters.
To find the distance traveled by the car during the 15 seconds, we can use the formula:
distance = initial velocity * time + (1/2) * acceleration * time^2
In this case, the initial velocity (v0) is 15 km/h, the final velocity (v) is 70 km/h, and the time (t) is 15 seconds. We need to find the acceleration (a) to calculate the distance.
First, let's convert the velocities from km/h to m/s, since the SI unit for acceleration is m/s^2.
Initial velocity (v0) = 15 km/h = (15 * 1000) / (60 * 60) = 4.17 m/s
Final velocity (v) = 70 km/h = (70 * 1000) / (60 * 60) = 19.44 m/s
Given that the acceleration is constant, we know that the change in velocity (Δv) is equal to the final velocity (v) minus the initial velocity (v0).
So, Δv = v - v0 = 19.44 m/s - 4.17 m/s = 15.27 m/s
Now, since we have both Δv and t, we can use the equation:
distance = v0 * t + (1/2) * a * t^2
Plugging in the values:
distance = (4.17 m/s) * 15 s + (1/2) * a * (15 s)^2
To solve for 'a', we need an additional equation. We know that
Δv = a * t
Plugging in the values:
15.27 m/s = a * 15 s
We can solve this equation for 'a':
a = 15.27 m/s / 15 s = 1.02 m/s^2
Now, we can substitute the value of 'a' into the distance equation:
distance = (4.17 m/s) * 15 s + (1/2) * (1.02 m/s^2) * (15 s)^2
Calculating this expression will give us the distance traveled by the car during the 15 seconds.