A car travelling at a uniform speed of 18 m/s. At time t = 0, the driver sees a child run out in front of the car.
At time t = 0.6 s the driver starts to apply the brakes. The car then decelerates uniformly, taking a further 3.0 s to stop. Calculate the distance travelled in the first 0.6 s of the
s = vt = 18 * 0.6 = 10.8 m
To calculate the distance traveled in the first 0.6 seconds, we need to use the formula for distance during uniform acceleration:
distance = initial velocity * time + (1/2) * acceleration * time^2
Since the car is initially traveling at a uniform speed of 18 m/s, the initial velocity (u) is 18 m/s. The time (t) is 0.6 seconds.
However, since the car starts to decelerate after 0.6 seconds, we cannot use this formula directly. Instead, we need to calculate the distance traveled during the first 0.6 seconds using the formula for uniform motion:
distance = speed * time
Plugging in the values:
distance = 18 m/s * 0.6 s
distance = 10.8 meters
Therefore, the car travels 10.8 meters in the first 0.6 seconds.
To calculate the distance traveled in the first 0.6 seconds, we need to find the initial distance covered by the car before the driver starts to apply the brakes and the distance covered during the period of time when the brakes are applied.
First, let's find the initial distance covered by the car. Since the car is traveling at a uniform speed of 18 m/s, we can use the formula:
Distance = Speed × Time
Distance = 18 m/s × 0.6 s
Distance = 10.8 meters
So, before the driver starts applying the brakes, the car has traveled 10.8 meters.
Next, let's find the distance covered during the period of time when the brakes are applied. The car decelerates uniformly, so we can use the formula:
Distance = (Initial Velocity × Time) + (0.5 × Acceleration × Time^2)
Here, the initial velocity is 18 m/s, the time is 3.0 seconds (since the car takes 3.0 seconds to stop), and the acceleration is the deceleration caused by the brakes.
To find the deceleration, we can use the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
Since the car comes to a stop, the final velocity is 0 m/s, and the time is 3.0 seconds.
Acceleration = (0 m/s - 18 m/s) / 3.0 s
Acceleration = -6 m/s^2
(Note: The negative sign indicates deceleration in the opposite direction to the initial velocity.)
Now, we can substitute the values into the formula for distance:
Distance = (18 m/s × 3.0 s) + (0.5 × -6 m/s^2 × (3.0 s)^2)
Distance = 54 meters + (-27 meters)
Distance = 27 meters
Therefore, the distance covered during the period of time when the brakes are applied is 27 meters.
Finally, to find the total distance traveled in the first 0.6 seconds, we can add the initial distance covered to the distance covered during the braking period:
Total Distance = Initial Distance + Distance during Braking
Total Distance = 10.8 meters + 27 meters
Total Distance = 37.8 meters
Therefore, the distance traveled in the first 0.6 seconds is 37.8 meters.