The maker of an automobile advertises that it takes 11 seconds to accelerate from 15 kilometers per hour to 90 kilometers per hour. Assuming constant acceleration, compute the following.
What is the distance the car travels during the 11 seconds (Round your answer to two decimal places.)?
a = 75 km/hr/s
= 20.833 m/s^2
s = vt + 1/2 at^2 = 4.1667(11) + (1/2)(20.833)(11^2) = 1306.23 m
To calculate the distance the car travels during the 11 seconds, we need to use the formula for distance traveled with constant acceleration:
distance = initial velocity * time + 0.5 * acceleration * time^2
First, we need to find the acceleration of the car. We know the initial velocity is 15 kilometers per hour, and the final velocity is 90 kilometers per hour. Since the time is constant (11 seconds), we can use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
Plugging in the values, we get:
acceleration = (90 km/h - 15 km/h) / 11 s
Next, we convert the velocities from kilometers per hour to meters per second, since the formula requires SI units:
initial velocity = 15 km/h * (1000 m/1 km) * (1 h/3600 s)
final velocity = 90 km/h * (1000 m/1 km) * (1 h/3600 s)
Substituting these values into the acceleration formula:
acceleration = (90 km/h * (1000 m/1 km) * (1 h/3600 s) - 15 km/h * (1000 m/1 km) * (1 h/3600 s)) / 11 s
Now that we have the acceleration, we can plug it into the formula for distance:
distance = 15 km/h * (1000 m/1 km) * (1 h/3600 s) * 11 s + 0.5 * acceleration * (11 s)^2
Simplifying and converting units:
distance = 15 * (1000/3600) * 11 + 0.5 * acceleration * (11)^2
Finally, we can calculate the distance:
distance = 13.75 + 0.5 * acceleration * 121
Now, all that's left is to substitute the value we found for acceleration and solve for distance.