A car is traveling 20m/s when the driver sees a child standing in the road. He takes 0.8s to react, then steps on the brakes and slows at 7.0m/s^2. How far does the car go before it stops?

i don't know where to start.

First figure out how far the car went in those first .8 seconds at 20 m/s

Then do the deacceleration problem

a = -7 m/s^2
vo = 20

v = v0 + a t = 20 - 7 t
so use that to find t when stopped, v = 0
0 = 20 - 7 t
solve for t, that is how long it deaccelerated to stop. Then use that t in
x = x0 + 20 t -(1/2)(7) t^2
that xo, the initial position, is the distance you got from the .8 second reaction time.

13.76m

To find the distance the car travels before it stops, we can divide the motion into two parts: the reaction time and braking time.

First, we need to determine the distance covered during the reaction time. The formula to calculate this distance is:

Distance = Initial velocity * Reaction time

In this case, the initial velocity is 20m/s, and the reaction time is 0.8s. Plugging these values into the formula, we get:

Distance (reaction time) = 20m/s * 0.8s = 16m

So during the reaction time, the car travels 16 meters.

Next, we need to determine the distance covered during the braking time. The formula to calculate this distance is:

Distance = (Initial velocity * Braking time) + (0.5 * Acceleration * Braking time^2)

In this case, the initial velocity is 20m/s, the acceleration (deceleration in this case) is -7.0m/s^2, and we want to find the distance covered when the car comes to a stop, which means the final velocity will be 0.

Since the final velocity is 0, we can rearrange the formula as follows:

0 = 20m/s + (-7.0m/s^2) * Braking time

Solving for the braking time, we get:

Braking time = -20m/s / (-7.0m/s^2) = 2.86s

Now, we can plug this braking time into the distance formula to find the distance covered during braking:

Distance (braking time) = (20m/s * 2.86s) + (0.5 * -7.0m/s^2 * (2.86s)^2)

Calculating this will give us the distance covered:

Distance (braking time) = 57.2m + (-28.55m) = 28.65m

Therefore, the distance covered during the braking time is 28.65 meters.

To find the total distance, we sum up the distance traveled during the reaction time and the braking time:

Total distance = Distance (reaction time) + Distance (braking time)
Total distance = 16m + 28.65m = 44.65m

So, the car will travel approximately 44.65 meters before it comes to a stop.