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.
conversion:26.39 m/s
v=v(i)+at
v has to be zero because she is going to stop. initial is 26.39 m/s
0=26.39 m/s+(-4.0)t
solve for t and add then add 1 sec(reaction time).
but then
1 second * initial speed + (1/2)(4)t^2
To determine the stopping distance of Sasha's car, we need to calculate two distances: the distance traveled during Sasha's reaction time and the distance traveled during the deceleration.
First, let's calculate the distance traveled during Sasha's reaction time. Sasha's reaction time is given as 1.0 second, which is the time between seeing the antelope and starting to brake.
During this time, the car will continue moving at its initial speed. To find the distance traveled, we need to convert the initial speed from km/hr to m/s.
Given:
Initial speed (v₀) = 95 km/hr = (95 × 1000) m/ (60 × 60) s = 26.39 m/s
Reaction time (t) = 1.0 s
Distance traveled during reaction time (dᵣ) = v₀ × t
Substituting the values:
dᵣ = 26.39 m/s × 1.0 s = 26.39 m
Now, let's calculate the distance traveled during the deceleration. Sasha's car experiences an acceleration of -4.0 m/s², which means it is slowing down.
Using the following kinematic equation:
d = (v² - v₀²) / 2a
Where:
d = distance traveled during deceleration
v = final velocity (0 m/s, as the car comes to a stop)
v₀ = initial velocity (26.39 m/s)
a = acceleration (-4.0 m/s²)
Substituting the values:
0 = (v² - (26.39 m/s)²) / (2 × -4.0 m/s²)
Rearranging the equation:
(v² - (26.39 m/s)²) = 0
(v² - 696.7921 m²) = 0
v² = 696.7921 m²
v ≈ 26.39 m/s (approximate value)
Now, we have the final velocity (v = 26.39 m/s), which is 0 m/s as the car comes to a stop.
To find the distance traveled (dₐ) during deceleration:
dₐ = (v - v₀) / 2a
Substituting the values:
dₐ = (0 - 26.39 m/s) / (2 × -4.0 m/s²)
dₐ = -26.39 m/s / (-8.0 m/s²)
dₐ ≈ 3.3 m (approximate value)
Finally, to calculate the total stopping distance (d_total), we sum the distance traveled during Sasha's reaction time (dᵣ) and the distance traveled during deceleration (dₐ):
d_total = dᵣ + dₐ
d_total ≈ 26.39 m + 3.3 m
d_total ≈ 29.69 m
Therefore, Sasha's car will require a stopping distance of approximately 29.69 meters from the moment she sees the antelope until her car comes to a complete stop.