Question

madeleinejames20 · Accepted Answer

To find the stopping distance of the car, we need to calculate the distance it travels during the reaction time and the distance it travels while decelerating.
First, let's calculate the distance traveled during the reaction time. We can use the formula:

d_{reaction} = v \cdot t

where:
-

d_{reaction}

is the distance traveled during the reaction time
-

v

is the initial velocity of the car
-

t

is the reaction time
Substituting the given values:

d_{reaction} = 20.0 m/s \cdot 0.530 s

d_{reaction} = 10.6 m

Next, let's calculate the distance traveled while decelerating. We can use the equation of motion:

v^{2} = u^{2} + 2 a s

where:
-

v

is the final velocity (which is 0 since the car stops)
-

u

is the initial velocity
-

a

is the acceleration (deceleration in this case)
-

s

is the stopping distance
Rearranging the equation, we have:

s = \frac{v^{2} - u^{2}}{2 a}

Substituting the given values:

s = \frac{0^{2} - (20.0 m/s)^{2}}{2 \cdot (- 7.00 {m/s}^{2})}

s = \frac{- 400.0 m^{2} / s^{2}}{- 14.00 {m/s}^{2}}

s = 28.6 m

Therefore, the stopping distance of the car, as measured from the point where the driver first notices the red light, is

10.6 m + 28.6 m = 39.2 m

.

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