A stationary ball starts rolling down a hill, and after 5s it reaches a speed of 12m/s. From here the ground levels off, and the ball continues at this speed for 3 more seconds. Plot this on a velocity-time diagram.
First we need to draw a velocity-time diagram, which has time on the x-axis, or bottom, and velocity on the y-axis, or left.The ball begins from a stop, so we can draw a dot at (0,0). It accelerates until it reaches 12m/s after 5 seconds, so another dot at (5,12). We can then connect these two points. As the ball continues for 3 more seconds, we can just draw a dot at (8,12) and connect with a straight line to the right.If we wanted to calculate acceleration, we just need to find the slope of the line in the first section, which is rise over run, or 12/5, or 2.4m/s2.To find the distance the ball travels, we need to find the area of each part of the graph. So the first section is a triangle, which is 1/2 * base * height, or 1/2 * 5 * 12, which is 30m. The second section is a square, so just height * base. This is 12 * 3, or 36m. Adding these we get 30 + 36 which is 66m.
