Question

A skateboarder is moving at a constant speed of 1.75 m/s when she starts up an incline that causes her to slow down with a constant acceleration of -0.20 m/s². How much time elapses from when she begins to slow down until she begins to move back down the incline?

Answer 1

The skateboarder takes 8.75 seconds to come to a stop. The total time elapsed from when she begins to slow down until she begins to move back down the incline is 17.5 seconds.

Step-by-step explanation:

To determine the time elapse, we can use the equations of motion. Let's first find the time it takes for the skateboarder to come to a stop. The initial velocity (u) is 1.75 m/s, and the acceleration (a) is -0.20 m/s². We can use the equation v = u + at, where v is the final velocity and t is the time. Since the skateboarder comes to a stop, the final velocity is 0. Plugging in the values, we get 0 = 1.75 + (-0.20)t, which simplifies to t = 1.75 / 0.20 = 8.75 seconds. Therefore, it takes 8.75 seconds for the skateboarder to come to a stop.

Since the skateboarder starts slowing down from the beginning of the incline and the question asks for the time until she begins to move back down the incline (in other words, the time until the skateboarder stops slowing down), the total time elapsed would be the double of the time it takes to come to a stop. Therefore, the time elapsed from when she begins to slow down until she begins to move back down the incline is 2 times 8.75 seconds, which is 17.5 seconds.