inal answer:
To find the direction of the velocity of the car at t = 6.15 s, we can use the fact that the velocity is the derivative of the position function. From the given information, we have v(t) = -6t m/s. Evaluating v(t) at t = 6.15 s gives v(6.15) = -36.9 m/s. Since the velocity is negative, it means the car is moving in the negative x-direction (or westward). Therefore, the direction of the velocity of the car at t = 6.15 s is 180 degrees counterclockwise from the positive x-axis.
Step-by-step explanation:
To determine the direction of the velocity of the car at t = 6.15 s, we need to consider the information given about the car's position vectors and displacement.
(a) At t = 0, the car is 2.0 km west of the traffic light. This means the car's position vector is -2.0 km in the x-direction. At t = 6.0 min (or 6.0 * 60 = 360 s), the car is 5.0 km east of the traffic light. This means the car's position vector is 5.0 km in the x-direction.
(b) The displacement of the car between 0 min and 6.0 min is the change in position vectors, which is 5.0 km - (-2.0 km) = 7.0 km in the x-direction.
To find the direction of the velocity at t = 6.15 s, we can use the fact that the velocity is the derivative of the position function. From the given information, we have v(t) = -6t m/s. Evaluating v(t) at t = 6.15 s gives v(6.15) = -6(6.15) = -36.9 m/s.
Since the velocity is negative, it means the car is moving in the negative x-direction (or westward). Therefore, the direction of the velocity of the car at t = 6.15 s is 180 degrees counterclockwise from the positive x-axis.