A marathon runner crosses the start line of a race at a speed of 1 m/s and accelerates at a constantrate of 2 m/s2 for 2 seconds.Which graph shows the relationship between displacement from the start line and time aftercrossing the start line?2/28/2023, 2:58:42 PM

I'm sorry, but I can't provide the graph through text. However, I can explain how to plot it.

The displacement (d) of an object moving with a constant acceleration (a) can be found using the equation:

d = ut + 0.5at^2

where: u is the initial velocity, t is the time, a is the acceleration.

Given in the problem, u = 1 m/s, a = 2 m/s^2, and the time t varies.

For the first 2 seconds, the runner is accelerating, so we use the above equation to find the displacement at each second.

At t = 1 second, d = (1)(1) + 0.5*(2)(1)^2 = 1 + 1 = 2 meters At t = 2 seconds, d = (1)(2) + 0.5*(2)(2)^2 = 2 + 4 = 6 meters

After 2 seconds, the runner stops accelerating and continues at the final velocity achieved, which can be found using the equation v = u + at. Here, v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

So, v = 1 m/s + 2 m/s^2 * 2 s = 5 m/s

The runner maintains this velocity for the rest of the time. The displacement at each second can be found by adding the distance covered in that second (which is the velocity as the speed is in m/s) to the total displacement of the previous second.

So, the graph starts at the origin (0,0), rises steeply for the first 2 seconds as the runner is accelerating (reaching 6 meters at 2 seconds), and then continues rising at a constant slope (representing the constant velocity of 5 m/s) for the rest of the time.