when the cart rolls down the track and collides with the force sensor why is the area under the curve in the force versus time graph positive but the calculated impulse on the cart negative

A 156-gram baseball is hit toward the left by a bat. The magnitude of the force the bat exerts on the ball as a function of time is shown in (Figure 1). a) find the magnitude of the impulse that the bat impart to the ball (N*s) b)Find the direction of the impulse that the bat imparts to the ball c)Find the magnitude of the ball's velocity just after it is hit by the bat if the ball is initially at rest d)find the direction of the ball's velocity just after it is hit by the bat if the ball is initially at rest e)find the magnitude of the ball's velocity just after it is hit by the bat if the ball is initially moving to the right at 31 m/s  f)Find the direction of the ball's velocity just after it is hit by the bat if the ball is initially moving to the right at 31.0 m/s.

You hold a beach ball above your head and then throw it upward. Represent the motion of the ball with an impulse-momentum bar chart: (a) For the ball as the system (b) For the ball and Earth as the system

Principle of __ provides a direct means of obtaining the particle’s final velocity after a specified time period when the particle’s initial velocity is known and the forces acting on the particle are either constant or can be expressed as functions of time. a. work and energy b. linear impulse and momentum c. angular impulse and momentum d. conservation of energy e. conservation of momentum

A force platform sensor used to measure the force of impact a 65.0 kg person makes with it after jumping down from a height of 0.600 m.  During the contact time of 0 to 0.800 s, the platform records an average force on it of -1226.67 N. What impulse did the person receive from the platform? What was the velocity of the person right before they hit the platform?  Neglect air resistance. What was the velocity of the person right after they left the platform? What was the average net force acting on the person? Using your answer from (d), determine the average contact force acting on the person.

For Number 8. please draw a diagram and do the math to explain the momentum For Number 9. please also do the math to show the relations between impulse and momentum Finally for 10, please show how momentum and impulse relate to the Force-time graph shown.

How does the Impulse compare to the change in momentum? Write an equation to show the relationship between Impulse and Change in Momentum.