a driver in a car traveling at a speed of 21.8 m/s sees a cat 101m away on the road. How long will it take for the car to accelarate uniformly to a stop in exactly 99m?

9.08

To find the time it takes for the car to accelerate uniformly to a stop, we can use the equations of motion. Let's break down the problem step by step:

1. Convert the speed to the initial velocity (u) in meters per second:
u = 21.8 m/s

2. Convert the distance to the final distance (s) in meters:
s = 99 m

3. Determine the acceleration (a) using the following equation:
v^2 = u^2 + 2as, where v is the final velocity (0 m/s),
a is the acceleration, u is the initial velocity, and s is the distance. Rearranging the equation, we get:
a = (v^2 - u^2) / (2s)
Substituting the values, we find:
a = (0 - (21.8)^2) / (2 * 99)

4. Calculate the time (t) using the equation:
v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Rearranging the equation, we get:
t = (v - u) / a
Substituting the values, we find:
t = (0 - 21.8) / ((0 - (21.8)^2) / (2 * 99))

Now let's calculate the acceleration and the time:

a = (0 - (21.8)^2) / (2 * 99)
a ≈ -10.94 m/s^2

t = (0 - 21.8) / ((0 - (21.8)^2) / (2 * 99))
t ≈ -1.991 s (Keep in mind that the negative sign indicates the car is decelerating.)

Therefore, it will take approximately 1.991 seconds for the car to uniformly accelerate to a stop in exactly 99 meters.

Use

v²-u²=2aS
where S=distance, 99m
a=acceleration to be found
v=final velocity, 0 m/s
u=initial velocity, 21.8 m/s
Solve for a.

-2.400