a person is driving unsafely on the highway at a speed of 145km/h and has to slam on the brakes in order to avoid a collision. the brakes can slow down the car at a rate of 10.4m/s^2. from the moment the car starts to slow down, how long will it take to stop?
To solve this problem, we can use the equations of motion. The car is initially traveling at a speed of 145 km/h, which can be converted to m/s by dividing by 3.6:
Initial speed (u) = 145 km/h = (145/3.6) m/s = 40.28 m/s
The car comes to rest, so the final speed (v) is 0 m/s.
The acceleration (a) of the car is given as -10.4 m/s^2 because it is slowing down (deceleration).
Using the equation: v = u + at
0 = 40.28 + (-10.4)t
Rearranging the equation, we have:
10.4t = 40.28
t = 40.28 / 10.4
t ≈ 3.87 seconds
Therefore, it will take approximately 3.87 seconds for the car to stop.
To find out how long it will take for the car to stop, we can use the following steps:
Step 1: Convert the speed from km/h to m/s.
Given speed = 145 km/h
To convert km/h to m/s, we can use the conversion factor 1 km/h = 0.2778 m/s.
Speed in m/s = 145 km/h * 0.2778 m/s/km/h = 40.28 m/s (approximately)
Step 2: Use the formula to calculate the time taken to stop.
Given acceleration = 10.4 m/s^2 (negative because it's deceleration)
Initial speed = 40.28 m/s
Time taken to stop = (Final speed - Initial speed) / Acceleration
Final speed is 0 m/s as the car comes to a stop.
Time taken to stop = (0 - 40.28) / (-10.4)
Time taken to stop ≈ 3.88 seconds
Therefore, it will take approximately 3.88 seconds for the car to come to a complete stop after applying the brakes.
To determine how long it will take for the car to stop, we need to consider the initial speed of the car, the deceleration rate of the brakes, and the formula for calculating time using acceleration.
The initial speed of the car is given as 145 km/h. We need to convert this speed to meters per second (m/s) since the acceleration is given in m/s^2.
1. Convert the speed from km/h to m/s:
145 km/h = (145 * 1000m) / (3600s)
= 40.28 m/s (rounded to two decimal places)
Now, we have the initial speed (u = 40.28 m/s) and the deceleration rate of the brakes (a = -10.4 m/s^2, negative because it is decelerating).
We can use the formula for calculating time (t) using acceleration (a):
t = (v - u) / a
Where:
v is the final velocity (0 m/s, since the car comes to a stop)
u is the initial velocity (40.28 m/s)
a is the deceleration rate (-10.4 m/s^2)
Plug in the values into the formula:
t = (0 - 40.28) / (-10.4)
t = 3.88 seconds (rounded to two decimal places)
Therefore, it will take approximately 3.88 seconds for the car to stop after the brakes are applied.