A car traveling at 91.0 km/h approaches the turnoff for a restaurant 30.0 m ahead. If the driver slams on the brakes with an acceleration of -6.40 m/s^2, what will her stopping distance be?
The stopping distance can be calculated using the equation d = (v^2)/(2a), where d is the stopping distance, v is the initial velocity, and a is the acceleration. Plugging in the given values, we get d = (91.0 km/h)^2/(2(-6.40 m/s^2)) = 5,837.5 m.
To calculate the stopping distance of the car, we need to analyze the motion of the car using the equations of motion. We can use the equation:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, as the car comes to a stop)
u = initial velocity (91.0 km/h, which needs to be converted to m/s)
a = acceleration (-6.40 m/s^2)
s = displacement (stopping distance, what we need to find)
To convert the velocity from km/h to m/s, we can use the following conversion factor:
1 km/h = 1000 m/3600 s
Let's convert the initial velocity:
u = (91.0 km/h) * (1000 m/3600 s)
u = 25.28 m/s
Now that we have the values, we can plug them into the equation:
0^2 = (25.28 m/s)^2 + 2 * (-6.40 m/s^2) * s
Simplifying the equation:
0 = 639.54 m^2/s^2 - 12.8 m/s^2 * s
Rearranging the equation to solve for s:
12.8 m/s^2 * s = 639.54 m^2/s^2
s = 639.54 m^2/s^2 / 12.8 m/s^2
s = 49.97 m
Therefore, the stopping distance of the car will be approximately 49.97 meters.
To find the stopping distance of the car, we need to consider the initial velocity, acceleration, and the distance to the turnoff.
First, let's convert the initial velocity from kilometers per hour (km/h) to meters per second (m/s). We can do this by multiplying the given value by 1000/3600 since there are 1000 meters in a kilometer and 3600 seconds in an hour.
Initial velocity (V0) = 91.0 km/h * (1000 m/1 km) * (1 h/3600 s)
V0 = 25.3 m/s (rounded to two decimal places)
Next, we can apply the kinematic equation to find the stopping distance:
Vf^2 = V0^2 + 2 * a * d
Where:
Vf = final velocity (which is 0 m/s since the car comes to a stop)
V0 = initial velocity (25.3 m/s)
a = acceleration (-6.40 m/s^2)
d = stopping distance (what we want to find)
Rearranging the equation to solve for d:
d = (Vf^2 - V0^2) / (2 * a)
Substituting the given values into the equation:
d = (0 - (25.3)^2) / (2 * (-6.40))
d = (0 - 640.09) / (-12.80)
d = 50.01 meters (rounded to two decimal places)
Therefore, the stopping distance of the car will be 50.01 meters.