To find the retardation (deceleration) of the car, we can use the following formula:
retardation = (final velocity - initial velocity) / time
Given: Initial velocity (u) = 45 km/h Final velocity (v) = 0 km/h (since the car comes to rest) Time (t) = 3 seconds
First, let's convert the initial velocity from km/h to m/s:
45 km/h = (45 * 1000) / 3600 m/s = 12.5 m/s
Now we can calculate the retardation:
retardation = (0 - 12.5) m/s / 3 s = -12.5/3 m/s² ≈ -4.17 m/s²
Note: The negative sign indicates deceleration or retardation.
To find the distance covered during this deceleration, we can use the following formula:
distance = (initial velocity * time) + (0.5 * retardation * time²)
Plugging in the values:
distance = (12.5 m/s * 3 s) + (0.5 * (-4.17 m/s²) * (3 s)² distance = 37.5 m + (-0.5 * 4.17 m/s² * 9 s²) distance = 37.5 m - 18.73 m distance ≈ 18.77 m
Therefore, the car moves approximately 18.77 meters before coming to rest.