When a vehicle takes off abruptly, you will jerk backward. To gain a better comprehension of the process,  you place a box on a frictionless surface at the back of a pick-up truck. There is no mechanism to secure the box. Explain what happens when the pick-up truck takes off.

An 8.50 kg trolley is accelerating in a straight line in the x-axis direction. The acceleration of the trolley as a function of time is shown in the graph below. Determine the times when the trolley experiences a constant net force. 

Find the velocity of a 2.0-kg block at t = 3.0s, initially at rest, when subjected to two forces: $\overrightarrow{F_1}$ = (17$\overrightarrow{i}$ + 13$\overrightarrow{j}$)N, $\overrightarrow{F_2}$ = (-11$\overrightarrow{i}$ + 23$\overrightarrow{j}$)N.

While going on a rescue operation, a soldier is hanging from a long rope to a helicopter, that is traveling eastward horizontally to lift people to rescue from a recent flood-affected area. If the helicopter is speeding up uniformly, then draw a clearly labeled free-body diagram for the soldier.

A lady with a container on her head rises up at a uniform speed from a crouching posture. Specify the objects that make up the system.

Make the following drawings i) motion diagram ii) force identification diagram iii) free-body diagram for a spaceship launched vertically upward that experiences significant air resistance.

A crash test dummy equipped with a force sensor is used to measure the impact force on a passenger during a frontal collision. The 55.00-kg dummy is buckled up with a seat belt. The car, initially moving at a speed of 60.00 km/h, collides with a thick wall. The airbag is deployed, and brings the dummy to rest at a distance of 125.0 cm. Determine the magnitude of the impact force on the dummy from the airbag as measured by the force sensor.

A 16-g pebble is thrown straight into a pile of sand at a speed of 370 m/s. After traveling 10 cm into the sand, the pebble stops. Calculate using kinematics and dynamics, the average force exerted by the sand onto the pebble.

Consider a skydiver with a mass of 70.0 kg falling vertically from a plane. As the skydiver descends, they experience air resistance, which increases as their velocity increases. The drag force acting on the skydiver can be described by the equation F_D = −cv², where v is the velocity of the skydiver and c is the drag coefficient. Determine the terminal velocity of the skydiver.

Shown below are three boats being pulled along the x-axis on a frictionless surface via ropes. If the magnitude of the pull force applied is 480 N, calculate the tension in each rope.

A person draws a bucket of water from a well, where the bucket is accelerating at 4.00 m/s² upwards. The rope attached to the bucket pass over a light pulley and has a tension of 20.0 N. Calculate the mass of the bucket of water.

A construction crane lifts a steel girder with a mass of 800 kg at an acceleration of 0.20g to a certain height on a building site. Calculate the tension in the lifting cable while the girder is accelerating.