Ann is driving down a street at 50 km/h. suddenly a child runs into the street. if it takes ann .75 seconds to react and apply the brakes. how many meters will ann have moved before she begins to slow down? If she slows down at a rate of 1.5m/s^2, how long will it take her to stop?
change 50km/hr to m/s
50km/hr*1hr/3600sec*1000m/km
then distance=speed*time
time to stop:
vf=vi+at where a=-1.5m/s^2, vf=0, vi is above speed in m/s
To find out how far Ann has moved before she begins to slow down, we need to calculate her reaction distance. The reaction distance is the distance covered by a vehicle during the driver's reaction time.
Given that Ann's reaction time is 0.75 seconds and her speed is 50 km/h, we first need to convert the speed from km/h to m/s. To do that, we divide the speed by 3.6 (since 1 km/h = 1/3.6 m/s).
The speed in m/s is:
50 km/h ÷ 3.6 = 13.9 m/s (rounding to one decimal place)
Now, to find the reaction distance, we multiply the speed by the reaction time:
Reaction distance = Speed × Reaction time
Reaction distance = 13.9 m/s × 0.75 s
Reaction distance ≈ 10.4 meters (rounded to one decimal place)
So, Ann will have moved approximately 10.4 meters before she begins to slow down.
Next, let's calculate how long it will take Ann to stop. We have the deacceleration rate (1.5 m/s^2) and we can assume that Ann is slowing down uniformly.
To find the time it takes for Ann to stop, we use the following formula:
v = u + at
Where:
v = final velocity (0 m/s since she stops)
u = initial velocity (13.9 m/s)
a = acceleration (1.5 m/s^2)
t = time
Rearranging the formula to solve for time (t), we get:
t = (v - u) / a
Plugging in the values, we have:
t = (0 m/s - 13.9 m/s) / (-1.5 m/s^2)
t = 13.9 m/s / 1.5 m/s^2
t ≈ 9.3 seconds (rounded to one decimal place)
Therefore, it will take Ann approximately 9.3 seconds to stop.