A car is initailly travelling at 50.0km/h. The brakes are applied and the car stops over a 35m distance. What was magnitude of the car's acceleraion while it was braking?
I don't know what formula to use.
V^2 = Vo^2 + 2a*d
V = 0
Vo = 50km/h = 50000m/3600s = 13.89 m/s
d = 35 m.
Solve for a. It will be negative.
To find the magnitude of the car's acceleration while braking, you can use the following formula:
a = (v^2 - u^2) / (2 * s)
Where:
a = acceleration (magnitude)
v = final velocity (0 m/s since the car stops)
u = initial velocity (50.0 km/h = 13.9 m/s)
s = distance traveled (35 m)
First, convert the initial velocity from km/h to m/s:
u = 50.0 km/h * (1000 m / 1 km) * (1 h / 3600 s)
u = 13.9 m/s
Now, substitute the values into the formula:
a = (0^2 - 13.9^2) / (2 * 35)
a = (-193.21) / 70
a ≈ -2.76 m/s²
Therefore, the magnitude of the car's acceleration while braking is approximately 2.76 m/s² in the negative direction.
To calculate the magnitude of the car's acceleration while braking, you can use the following formula:
acceleration = change in velocity / time
However, in this case, we are not directly given the time it took for the car to stop. Instead, we are given the initial speed (50.0 km/h = 13.9 m/s) and the distance over which the car stops (35 m).
To find the time it took for the car to stop, we can use another formula:
distance = initial velocity * time + (1/2) * acceleration * time^2
Since the car starts from rest (initial velocity = 0), the equation becomes:
distance = (1/2) * acceleration * time^2
Rearranging the equation, we get:
time = sqrt(2 * distance / acceleration)
Now let's substitute the given values into the equation. The distance is 35 m. Initially, the car was traveling at 13.9 m/s, which is equivalent to 0 m/s (since the car came to a stop).
Using the above equation, we can solve for time:
time = sqrt(2 * 35 / acceleration)
Next, let's calculate the time it took for the car to stop.