A 0.165-kg ball, moving in the positive direction at 10 m/s, is acted on by the impulse shown in the graph below. What is the ball's speed at 4.0 s?
To find the ball's speed at 4.0 s, we need to use the concept of impulse and the formula for impulse-momentum.
Impulse (J) is calculated by multiplying the force acting on an object by the time the force is applied. It is also defined as the change in momentum (∆p) of an object.
The formula for impulse is:
J = ∆p = m∆v
Where:
J is the impulse
∆p is the change in momentum
m is the mass of the object
∆v is the change in velocity
In the given question, we have a graph representing the impulse, so we need to find the area under the impulse versus time graph to calculate the impulse.
To find the area of the graph, we can divide it into various shapes and calculate their individual areas. In this case, the graph seems to consist of a triangle and a rectangle.
The area of the triangle can be found using the formula:
Area of a triangle = 0.5 * base * height
The area of the rectangle can be found using the formula:
Area of a rectangle = length * width
By summing up the areas of the triangle and the rectangle, we can find the total impulse.
Once we have the impulse, we can use the formula J = ∆p = m∆v to find the change in velocity (∆v).
∆v = J / m
Finally, to find the ball's speed at 4.0 s, we need to add the change in velocity (∆v) to the initial velocity (10 m/s).
Ball's speed at 4.0 s = Initial velocity + ∆v