Question

A boat is drifting to the right with a speed of 5.0 m/s​ when the driver turns on the motor. The motor runs for 6.0s, causing a constant leftward acceleration of magnitude 4.0 m/s²​. What is the displacement of the boat over the 6.0s time interval? Provide the correct sign for your answer, using a coordinate system where rightward is positive. Round the answer to two significant digits.

Answer 1

The displacement of the boat over the 6.0s time interval is -7.0 m to the left.

Step-by-step explanation:

To find the displacement of the boat over the 6.0s time interval, we need to calculate the final velocity and then use it to find the displacement. The final velocity can be found using the equation: final velocity = initial velocity + (acceleration * time). In this case, the initial velocity is 5.0 m/s to the right, the acceleration is -4.0 m/s² to the left, and the time is 6.0s. Plugging these values into the equation, we get:
final velocity = 5.0 m/s - (4.0 m/s² * 6.0s) = -19.0 m/s.

The displacement is the change in position of the boat during the time interval, which is given by the equation: displacement = (initial velocity + final velocity) / 2 * time. Plugging in the values, we get:
displacement = (5.0 m/s + -19.0 m/s) / 2 * 6.0s = -42.0 m / 2 * 6.0s = -7.0 m.

Therefore, the displacement of the boat over the 6.0s time interval is

-7.0 m

to the left.