A Car is travelling at 20 km/s along a road . A child runs out into the road some ahead and the car driver steps on the brake pedal.What must the car's Acceleration be if the car is to stop just before it reaches the child?
missing data ... distance to child
To determine the car's required acceleration to stop just before reaching the child, we need to use the equations of motion.
Since we know the distance traveled by the car, we can calculate the time it takes for the car to reach the child.
First, we need to convert the velocity from km/s to m/s:
20 km/s = 20,000 m/s
Next, we can use the equation of motion:
d = ut + (1/2)at^2
Where:
d = distance traveled (unknown)
u = initial velocity = 20,000 m/s
a = acceleration (unknown)
t = time (unknown)
Since the car needs to stop just before reaching the child, the final velocity should be zero.
Therefore, we can write an additional equation:
v = u + at
0 = 20,000 + at
We can rearrange the second equation to solve for t:
t = -20,000/a
Substituting the value of t into the first equation:
d = (20,000)(-20,000/a) + (1/2)(a)((-20,000/a)^2)
d = 400,000,000/a + (1/2)(a)(400,000,000/a^2)
d = 400,000,000/a + 200,000,000/a
Now, we set the equation equal to the distance the child is ahead (let's assume it is x) and solve for a:
x = 400,000,000/a + 200,000,000/a
Multiplying both sides by 'a' to clear the denominator:
ax = 400,000,000 + 200,000,000
Simplifying further:
ax = 600,000,000
Finally, we can solve for a:
a = 600,000,000/x
Therefore, if the car is to stop just before reaching the child, the car's acceleration must be equal to 600,000,000 divided by the distance the child is ahead.