A vehicle traveling 63 km/h [E] accelerates 1.0 m/s2 [E] for 9.0s. Determine the displacement of the vehicle during this 9.0 s time interval.
s = vt + 1/2 at^2
in the direction of motion
To determine the displacement of the vehicle during the 9.0 s time interval, we can use the equation of motion:
displacement = initial velocity * time + 0.5 * acceleration * time^2
Given:
Initial velocity (u) = 63 km/h [E] = 63,000 m / 3600 s = 17.5 m/s [E]
Acceleration (a) = 1.0 m/s^2 [E]
Time (t) = 9.0 s
Plugging these values into the equation of motion:
displacement = (17.5 m/s [E]) * (9.0 s) + 0.5 * (1.0 m/s^2 [E]) * (9.0 s) ^ 2
First, we calculate the first term on the right side:
(17.5 m/s [E]) * (9.0 s) = 157.5 m [E]
Then, we calculate the second term on the right side:
0.5 * (1.0 m/s^2 [E]) * (9.0 s) ^ 2 = 0.5 * (1.0 m/s^2) * 81.0 s^2 = 40.5 m [E]
Now, we can sum up both terms:
displacement = 157.5 m [E] + 40.5 m [E] = 198.0 m [E]
Therefore, the displacement of the vehicle during the 9.0 s time interval is 198.0 meters east.
To determine the displacement of the vehicle during the 9.0s time interval, we can use the formula of displacement:
Displacement = Initial Velocity * Time + 0.5 * Acceleration * Time^2
Given:
Initial velocity (u) = 63 km/h [E]
Acceleration (a) = 1.0 m/s^2 [E]
Time (t) = 9.0s
First, let's convert the initial velocity from km/h to m/s:
1 km/h = (1 * 1000) m / (3600 * 1) s
1 km/h = 1000 m / 3600 s
1 km/h = 0.2778 m/s (approximately)
Therefore, the initial velocity (u) = 0.2778 m/s [E]
Now, we can substitute the values into the displacement formula:
Displacement = (0.2778 m/s) * (9.0s) + 0.5 * (1.0 m/s^2) * (9.0s)^2
Simplifying the equation:
Displacement = 2.5002 m + 0.5 * 1.0 m/s^2 * 81.0 s^2
Displacement = 2.5002 m + 0.5 * 81.0 m
Displacement = 2.5002 m + 40.5 m
Displacement = 43.0002 m
Therefore, the displacement of the vehicle during the 9.0s time interval is approximately 43.0002 meters.