A car is traveling at 65 km/hr. The brakes are applied and the car stops in 3 seconds. How far does it travel? Write down the given, unknown, formula, solution, and the final answer.
Given:
- Initial velocity (u) = 65 km/hr
- Time taken to stop (t) = 3 seconds
Unknown:
- Distance traveled (s)
Formula:
The formula used to calculate distance (s) when the initial velocity (u) and time taken (t) are known is:
s = (u * t) + (0.5 * a * t^2)
Solution:
Since the brakes are applied and the car comes to a stop, the final velocity (v) is 0 km/hr.
Using the formula, we can rewrite it as:
0 = (65 * t) + (0.5 * a * t^2)
We know that the final velocity (v) is defined as v = u + (a * t). Since the car comes to a stop, the final velocity is 0. Plugging in the values we have:
0 = 65 + (a * 3)
Simplifying the equation, we get:
0 = 65 + 3a
Rearranging the terms:
3a = -65
Solving for acceleration (a):
a = -65 / 3
Now, substituting the value of acceleration (a) and time (t) into the formula for distance (s):
s = (65 * 3) + (0.5 * (-65/3) * (3^2))
s = 195 - (0.5 * 65 * 3)
s = 195 - 97.5
s = 97.5 km
Final Answer:
The car travels a distance of 97.5 kilometers.