To find the ball's speed at 4.0 s, calculate the change in momentum by finding the area under the impulse-time graph. Set up the impulse-momentum equation to find the final momentum, and then divide the final momentum by the mass of the ball to find the final velocity. The ball's speed at 4.0 s is 13.1 m/s.
To determine the ball's speed at 4.0 s, we need to analyze the area under the impulse-time graph. The impulse is equal to the change in momentum of the ball. Using the impulse-momentum principle, we can calculate the change in momentum of the ball over the given time interval. The ball's initial momentum is given by mass times velocity, and the final momentum is obtained by multiplying the mass of the ball with its final velocity, which is what we need to find.
First, we calculate the change in momentum using the formula: Impulse = Change in momentum. The impulse is equal to the area under the graph, which can be divided into two sections: a rectangle and a triangle.
The rectangle's area is given by its base, which is the width of the rectangle, multiplied by its height. In this case, the width is 0.6 s, and the height is 0.2 N*s. Therefore, the rectangle's area is 0.12 N*s. The triangle's area can be calculated using the formula for the area of a triangle: 1/2 * base * height. The base of the triangle is also 0.6 s, and the height is 0.15 N*s. Thus, the triangle's area is 0.045 N*s. Finally, we sum up the areas of the rectangle and the triangle to find the total impulse, which is 0.165 N*s.
Now, we can use the principle of impulse-momentum to find the final velocity of the ball. The impulse is equal to the change in momentum, so we can set up the equation: final momentum - initial momentum = impulse. The ball's initial momentum is given as 0.150 kg * 12 m/s = 1.8 N*s, and the final momentum is 1.8 N*s + 0.165 N*s = 1.965 N*s.
To find the final velocity, we divide the final momentum by the mass of the ball: final velocity = final momentum / mass. Therefore, the ball's final velocity at 4.0 s is 1.965 N*s / 0.150 kg = 13.1 m/s.
The probable diagram is attached below.