A car moves at 12 m/s and coasts up a hill with a uniform acceleration of -1.4 m/s2
a)What is its displacement after 6.0 s
b)What is its displacement after 9.0 s?
To find the displacement of the car after a certain time, we can use the kinematic equation:
displacement = initial velocity * time + (1/2) * acceleration * time^2
Given:
initial velocity (u) = 12 m/s
acceleration (a) = -1.4 m/s^2
a) To find the displacement after 6.0 s, we can substitute the values into the equation:
displacement = 12 m/s * 6.0 s + (1/2) * (-1.4 m/s^2) * (6.0 s)^2
displacement = 72 m + (1/2) * (-1.4 m/s^2) * 36 s^2
displacement = 72 m + (-25.2 m)
displacement = 46.8 m
Therefore, the displacement of the car after 6.0 s is 46.8 m.
b) To find the displacement after 9.0 s, we can substitute the values into the equation:
displacement = 12 m/s * 9.0 s + (1/2) * (-1.4 m/s^2) * (9.0 s)^2
displacement = 108 m + (1/2) * (-1.4 m/s^2) * 81 s^2
displacement = 108 m + (-56.7 m)
displacement = 51.3 m
Therefore, the displacement of the car after 9.0 s is 51.3 m.
To solve these problems, we can use the equations of motion.
The equation for displacement when the acceleration is constant is:
x = x0 + v0 * t + (1/2) * a * t^2
Where:
x = displacement
x0 = initial displacement
v0 = initial velocity
t = time
a = acceleration
a) To find the displacement after 6.0 seconds, we need to know the initial displacement (x0), initial velocity (v0), and acceleration (a). The problem did not provide the initial displacement, so we assume it starts from rest (x0 = 0) since it does not mention otherwise. The initial velocity is given as 12 m/s and the acceleration as -1.4 m/s^2.
Plugging the values into the equation:
x = 0 + (12 * 6) + (1/2) * (-1.4) * (6)^2
Simplifying the equation:
x = 0 + 72 - 37.8
x = 34.2 meters
Therefore, the car's displacement after 6.0 seconds is 34.2 meters.
b) To find the displacement after 9.0 seconds, we use the same equation. Since the problem did not mention any changes, we assume it starts from the same initial conditions (x0 = 0, v0 = 12 m/s, a = -1.4 m/s^2).
Plugging the values into the equation:
x = 0 + (12 * 9) + (1/2) * (-1.4) * (9)^2
Simplifying the equation:
x = 0 + 108 - 56.7
x = 51.3 meters
Therefore, the car's displacement after 9.0 seconds is 51.3 meters.