The magnitude of the acceleration when the car is at point B is approximately 5.41 m/s². The direction of the acceleration is towards the east.
What is the magnitude and direction of the acceleration when the car is at point b?
v = s/t
v = 222 m / 41.0 s ≈ 5.41 m/s
Since the car is moving in a circular path, it experiences centripetal acceleration directed towards the center of the circle. The formula for centripetal acceleration is:
ac = v² / r
where r is the radius of the circle.
In this case, we don't know the exact radius, but we can express it in terms of the arc length and the central angle θ:
r = s / θ
The central angle θ can be calculated using the formula:
θ = s / r
Combining these equations, we get:
θ = s² / r²
Substituting s = 222 m, we get:
θ = 222² / ²
The acceleration at point B is the vector sum of the centripetal acceleration (ac) and the tangential acceleration (at). Tangential acceleration is directed along the tangent to the circle, and it causes the car to change its speed.
At point B, the car's direction is changing from eastward to northward, so the tangential acceleration is directed towards the north. Since the car's speed is constant, the tangential acceleration is zero.
Therefore, the magnitude of the acceleration (a) is equal to the magnitude of the centripetal acceleration (ac):
a = ac = v² / r
The direction of the acceleration is towards the center of the circle and perpendicular to the car's velocity vector. At point B, the car's velocity vector is directed towards the north. Therefore, the direction of the acceleration is towards the east.
The magnitude of the acceleration when the car is at point B is approximately 5.41 m/s². The direction of the acceleration is towards the east.