Sasha is driving straight and notices an antelope in the road a ways off. Determine the stopping distance (from the time she sees the antelope) for her car with an initial speed of 95 km/hr and an acceleration of -4.0 m/s2. Sasha's reaction time to start breaking is 1.0 second.
recall that the equation for distance is
s = vt + a/2 t^2
95 km/hr = 26.39 m/s
So, it will take 26.39/4 = 6 seconds of braking to stop.
s = 95*7 - 2*6^2 = 593 meters to stop
I guess she had good eyes, seeing an antelope at half a km away! Or, maybe she just hit it, or swerved past at the end...
sorry. 26.39/4 = 6.59
don't know how I got so far off. So, fix t and redo the calculation...
To determine the stopping distance for Sasha's car, we need to consider two components: the distance covered during Sasha's reaction time and the distance covered during the braking period.
First, let's find the distance covered during Sasha's reaction time. We know that Sasha's reaction time is 1.0 second, during which the car maintains its initial speed. The distance covered during this time can be calculated using the formula:
Distance = Initial velocity * Time
In this case, the initial velocity is 95 km/hr, which needs to be converted to m/s. We know that 1 km/hr is equal to 0.278 m/s. So, the initial velocity will be:
Initial velocity = 95 km/hr * 0.278 m/s = 26.41 m/s
Substituting the values into the formula:
Distance = 26.41 m/s * 1.0 s = 26.41 m
Now let's calculate the distance covered during the braking period. The acceleration of the car is -4.0 m/s^2 because it is decelerating. We can use the following kinematic equation to find the distance covered during braking:
Distance = (Final velocity^2 - Initial velocity^2) / (2 * acceleration)
The final velocity will be zero since the car comes to a stop. Substituting the values into the formula:
Distance = (0 - (26.41 m/s)^2) / (2 * -4.0 m/s^2)
= (-696.1681 m^2/s^2) / (-8.0 m/s^2)
= 87.021 m
To find the total stopping distance, we add the distance covered during Sasha's reaction time to the distance covered during braking:
Total stopping distance = Distance during reaction time + Distance during braking
= 26.41 m + 87.021 m
= 113.431 m
Therefore, the stopping distance for Sasha's car, from the time she sees the antelope, is 113.431 meters.