In a car accidnet involving a sports car, skid marks as long as 290 m were left by the car as it decelearted to a complete stop. The police report cited the speed of the car before breaking as beeing in excess of 100mph 161 km/m. Suppose that i took 10 seconds for the car to stop. Estimate the speed of the car before the brakes were applied
a is deacceleration
v = Vi - a t
which is = 0 at stop
0 = Vi -10 a
a = .1 Vi
X-Xi = d = Vi t - (1/2) a t^2
290 = Vi (10) - .5 a (100)
290 = 10 Vi -50 a
290 = 10 Vi -5 Vi
290 = 5 Vi
vi = 58 meters/second = .058 km/second
* 3600 seconds/hr = 209 km/hr
By the way How on earth was I to know this was a physics question from your title? You are just lucky Ik spreek Hollands.
To estimate the speed of the car before the brakes were applied, we can use the relationship between distance, time, and acceleration.
1. Convert the skid mark length from meters to kilometers:
290 m = 0.290 km
2. Convert the time taken to stop from seconds to hours:
10 seconds = 10/3600 hours (3600 seconds in an hour)
3. Use the formula for average acceleration:
acceleration = (final velocity - initial velocity) / time
4. Rearrange the formula to solve for initial velocity:
initial velocity = final velocity - (acceleration * time)
Given:
- Skid mark length (distance) = 0.290 km
- Time to stop (time) = 10/3600 hours (10 seconds converted to hours)
We need to calculate final velocity and acceleration. Since the car came to a complete stop, the final velocity is 0 km/h.
5. Calculate the acceleration:
acceleration = (final velocity - initial velocity) / time
Since the final velocity is 0 km/h, it becomes:
acceleration = -initial velocity / time
Substituting the values we have, the equation becomes:
acceleration = -initial velocity / (10/3600)
6. Rearrange the equation to solve for initial velocity:
-initial velocity = acceleration * (10/3600)
initial velocity = -acceleration * (10/3600)
Now, we need to determine the acceleration. We can use the formula for acceleration:
7. Given the initial velocity of the car was in excess of 100 mph (161 km/h), we can convert it to km/h:
initial velocity = 161 km/h
8. Convert the initial velocity from km/h to km/s:
initial velocity = 161 km/h * (1/3600) km/s
9. Calculate acceleration:
acceleration = (-161/3600) km/s / (10/3600) h
Simplifying:
acceleration = -161 / 10 km/s^2
10. Calculate the initial velocity:
initial velocity = -acceleration * (10/3600)
Substituting the value of acceleration:
initial velocity = -(-161/10) km/s^2 * (10/3600)
= 161/360 km/s
Finally, convert the initial velocity to km/h:
initial velocity = (161/360) km/s * (3600) s/h
= 161 km/h
Thus, the estimated speed of the car before the brakes were applied is 161 km/h.
To estimate the speed of the car before the brakes were applied, we can use the equation of motion for deceleration:
v² = u² + 2as
where:
v = final velocity (0 m/s since the car comes to a complete stop)
u = initial velocity (speed of the car before the brakes were applied)
a = acceleration (negative value representing deceleration)
s = distance traveled (290 m)
We know that the car took 10 seconds to stop, so the time it took to travel the distance can be calculated using the equation of motion:
s = ut + (1/2)at²
Rearranging the equation:
s = ut + (1/2)at²
290 = u(10) + (1/2)(-a)(10)²
290 = 10u - 50a (Equation 1)
Now, we also know that the speed of the car before braking was in excess of 100 mph or 161 km/h. We can convert this to m/s:
u > 100 mph = (100 * 1609.34) / 3600 = 44.704 m/s
Now, substituting the value of u into Equation 1:
290 = 10(44.704) - 50a
290 = 447.04 - 50a
50a = 447.04 - 290
50a = 157.04
a = 3.1408 m/s²
Now, to find the initial velocity (u), we can use the equation:
v = u + at
Since the final velocity (v) is 0:
0 = u + (3.1408)(10)
0 = u + 31.408
u = -31.408 m/s
The negative sign indicates that the car was moving in the opposite direction. Therefore, the estimate for the speed of the car before the brakes were applied is approximately 31.408 m/s or 113.0688 km/h.