A driver in a car traveling at a speed of

70 km/h sees a cat 129 m away on the road.
How long will it take for the car to accelerate uniformly to a stop in exactly 125 m?
Answer in units of s

The average speed, 35 km/h = 9.72 m/s, multiplied by the time, must equal 125 m.

Use that fact to solve for the time.

To find the time it takes for the car to accelerate uniformly to a stop, we need to make use of the equations of motion. Specifically, we can use the equation:

v^2 = u^2 + 2as

where:
v = final velocity (0 m/s in this case, since the car comes to a stop)
u = initial velocity (70 km/h = 19.44 m/s)
a = acceleration (which we need to find)
s = displacement (125 m)

First, let's convert the initial velocity from km/h to m/s:
u = 70 km/h * (1000 m/1 km) * (1 h/3600 s) = 19.44 m/s

Now, let's rearrange the equation to solve for acceleration (a):
a = (v^2 - u^2) / (2s)

Substituting the values we know:
a = (0^2 - 19.44^2) / (2 * 125)

a = (-19.44^2 / 250)

a = -298.59 m/s^2

The negative sign indicates that the car is decelerating.

Now, we can use another equation to find the time (t) it takes for the car to accelerate uniformly to a stop:

t = (v - u) / a

Substituting the values we know:
t = (0 - 19.44) / -298.59

t ≈ 0.065 s

Therefore, it will take approximately 0.065 seconds for the car to accelerate uniformly to a stop in exactly 125 m.