a driver traveling at 50 mph is 80 m from the wall ahead. if the driver applies the brakes immediately and begins slowing the vehicle at 10 m/s squared, find the distance from the stopping point to the wall.
1 mph = 5280*.3048/3600=0.44704 m/s
vi=50*.44704=22.352 m/s
vf=0
a=-10 m/s²
use kinematics equation
vf²=vi²+2aΔx
to solve for Δx.
Subtract Δx from 80m to get the distance from the wall.
25
Well, isn't it a classic situation of "brake it till you make it"! Let's do the math and find out the distance from the stopping point to the wall.
First, we need to convert the speed from miles per hour to meters per second. Since there are 1609.344 meters in a mile and 3600 seconds in an hour, we multiply 50 mph by (1609.344/3600) to get the speed in meters per second.
50 mph * (1609.344/3600) ≈ 22.35 m/s
Now, let's calculate the time it takes for the driver to stop. We can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the deceleration, and t is the time.
Since the final velocity is 0 (the driver stops), and the initial velocity is 22.35 m/s, the deceleration is -10 m/s^2 (negative because the vehicle is slowing down), and we're looking for the time, we can rearrange the formula to find t.
0 = 22.35 m/s + (-10 m/s^2) * t
Solving for t, we get t ≈ 2.24 seconds.
Now that we know how long it takes to stop, we can calculate the distance traveled during that time using the formula:
distance = initial velocity * time + 0.5 * acceleration * time^2
distance = 22.35 m/s * 2.24 s + 0.5 * (-10 m/s^2) * (2.24 s)^2
distance ≈ 49.99 meters
So, the distance from the stopping point to the wall is approximately 49.99 meters. That's one close call! I hope the driver didn't leave any skid marks!
To find the distance from the stopping point to the wall, we need to calculate the stopping distance of the vehicle.
Given:
Initial speed (u) = 50 mph
Final speed (v) = 0 mph (since the vehicle comes to a stop)
Acceleration (a) = -10 m/s² (negative because it's a deceleration)
Before proceeding with the calculations, we need to convert the initial speed from mph to m/s.
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, 50 mph = (50 * 1609.34) / 3600 = 22.35 m/s
Now, we can use the following formula to calculate the stopping distance (S):
v² = u² + 2as
Plugging in the values:
0² = (22.35)² + 2*(-10)*S
0 = 499.7225 - 20*S
20*S = 499.7225
S = 499.7225 / 20
S ≈ 24.99 meters
Therefore, the distance from the stopping point to the wall is approximately 24.99 meters.
To find the distance from the stopping point to the wall, we need to determine how long it takes for the vehicle to come to a complete stop. We can then use this time to calculate the distance traveled during that time.
First, let's convert the driver's initial speed from mph (miles per hour) to m/s (meters per second). Since 1 mile is equal to 1609.34 meters and 1 hour is equal to 3600 seconds, we have:
Speed = 50 mph = (50 * 1609.34) / 3600 m/s ≈ 22.35 m/s
Next, let's calculate the time it takes for the vehicle to stop. We can use the equation:
v = u + at
Where:
v is the final velocity (0 m/s, since the vehicle stops),
u is the initial velocity (22.35 m/s),
a is the deceleration (-10 m/s², since the vehicle is slowing down),
and t is the time.
0 = 22.35 + (-10) * t
Now, solve for t:
10t = 22.35
t = 22.35 / 10 ≈ 2.24 seconds
Therefore, it takes approximately 2.24 seconds for the vehicle to come to a complete stop.
To calculate the distance traveled during this time, we can use the equation:
s = ut + (1/2)at²
Where:
s is the distance traveled,
u is the initial velocity (22.35 m/s),
t is the time (2.24 seconds),
and a is the deceleration (-10 m/s²).
s = (22.35 * 2.24) + (1/2) * (-10) * (2.24)²
s ≈ 50.04 + (-25.12)
s ≈ 24.92 meters
Therefore, the distance from the stopping point to the wall is approximately 24.92 meters.