A driver in a car traveling at a speed of
72 km/h sees a cat 107 m away on the road.
How long will it take for the car to accelerate uniformly to a stop in exactly 104 m?
-1.923 m/s2
A driver in a car traveling at a speed of
73 km/h sees a cat 103 m away on the road.
How long will it take for the car to accelerate
uniformly to a stop in exactly 100 m?
To determine the time it takes for the car to accelerate uniformly to a stop in exactly 104 m, we can use the equations of motion.
Let's break down the problem and identify the given information:
Initial speed of the car (u) = 72 km/h
Distance to stop (s) = 104 m
Acceleration (a) = ?
We need to find the acceleration to calculate the time it takes for the car to stop.
First, convert the initial speed from km/h to m/s:
Initial speed (u) = 72 km/h = (72 * 1000) m/ (60 * 60) s = 20 m/s
Now, we can use the following equation of motion to find the acceleration:
v^2 = u^2 + 2as
The car comes to a stop when its final speed (v) is 0. Therefore, we can write the equation as:
0^2 = (20 m/s)^2 + 2a * 104 m
Simplifying the equation:
0 = 400 m^2/s^2 + 208a
Rearranging the equation to isolate the acceleration (a):
208a = -400 m^2/s^2
a = (-400 m^2/s^2) / 208
Calculate the value of acceleration:
a ≈ -1.92 m/s^2
The negative sign indicates that the car is decelerating.
Now that we have found the acceleration, we can use it to find the time (t) it takes for the car to stop.
We can use the following equation of motion:
v = u + at
Since we are looking for the time it takes for the car to stop, we can substitute v = 0:
0 = 20 m/s + (-1.92 m/s^2) * t
Simplifying the equation:
1.92 m/s^2 * t = 20 m/s
t = 20 m/s / 1.92 m/s^2
Calculating the value of time:
t ≈ 10.42 s
Therefore, it will take approximately 10.42 seconds for the car to accelerate uniformly to a stop in exactly 104 m.
72 km/hr *1000/3600 = 20 m/s
average speed during acceleration = (20+0)/2 = 10 m/s
104 = 10 m/s * time to stop
so
time = t = 10.4 seconds