Worksheet: Kinematics and Forces

In this worksheet, we will practice analyzing the resultant motion of objects that exert various forces and have various forces exerted on them.

Q1:

A constant 10 N horizontal force is applied to a 20 kg cart at rest on a level floor. If friction is negligible, what is the speed of the cart by the time it has been pushed 8.0 m?

Q2:

A 2.50-kg fireworks shell is fired straight up from a mortar and reaches a height of 110 m above the muzzle of the mortar.

Neglecting air resistance, calculate the shell’s velocity when it leaves the mortar.

The mortar itself is a tube 0.450 m long. Calculate the magnitude of the average acceleration of the shell in the tube as it goes from zero to the velocity at which it leaves the mortar.

  • A 2 . 4 9 × 1 0 m/s2
  • B 2 . 2 0 × 1 0 m/s2
  • C 2 . 3 2 × 1 0 m/s2
  • D 2 . 4 0 × 1 0 m/s2
  • E 2 . 1 1 × 1 0 m/s2

What is the magnitude of the average force on the shell in the mortar?

  • A 6 . 7 7 × 1 0 N
  • B 6 . 5 0 × 1 0 N
  • C 6 . 3 1 × 1 0 N
  • D 5 . 9 9 × 1 0 N
  • E 6 . 1 7 × 1 0 N

Q3:

A shot-putter throws a shot of mass 7.26 kg a horizontal distance of 22.2 m.

The shot is released from the shot-putter’s hand 2.20 m vertically above the ground and at an angle 4 5 . 0 above the horizontal. What is the initial speed of the shot?

While in the shot-putter’s hand, the shot is accelerated uniformly over a 1.20 m distance. What net force acted on the shot to accelerate it?

Q4:

A rocket sled accelerates at a rate of 49.0 m/s2. Its passenger has a mass of 75.0 kg.

Calculate the horizontal component of the force the seat exerts against his body.

  • A 3 . 8 0 × 1 0 N
  • B 3 . 9 3 × 1 0 N
  • C 3 . 3 3 × 1 0 N
  • D 3 . 6 8 × 1 0 N
  • E 3 . 5 1 × 1 0 N

Find the ratio of the magnitude of the horizontal component with the passenger’s weight.

Calculate the angle from the horizontal of the total force the seat exerts against his body.

Calculate the magnitude of the total force the seat exerts against his body.

  • A 3 . 7 5 × 1 0 N
  • B 3 . 5 2 × 1 0 N
  • C 3 . 6 6 × 1 0 N
  • D 3 . 5 9 × 1 0 N
  • E 3 . 7 1 × 1 0 N

Q5:

Two teenagers are pulling on ropes attached to a tree. The angle between the ropes is 3 0 . 0 . pulls with a force of 400 N in the positive 𝑥 -direction and pulls with a force of 300 N.

Find the component form of the net force.

  • A ( 6 6 0 + 1 5 0 ) i j N
  • B ( 6 6 0 + 3 5 0 ) i j N
  • C ( 6 7 0 + 1 7 0 ) i j N
  • D ( 7 6 0 1 0 0 ) i j N
  • E ( 7 0 0 + 1 5 0 ) i j N

Find the magnitude of the net force on the tree from the ropes.

Find the angle between the direction of the net force on the tree from the ropes and the direction of ’s rope.

Q6:

An 85.0 kg mass basketball player jumps vertically upward to catch a ball. The player lowers his body 0.240 m vertically downward and then accelerates vertically upward through this distance by straightening his legs. This player launches from the ground with a vertically upward speed sufficient to reach a height of 0.725 m.

At what speed is the basketball player moving vertically upward at the instant that he loses contact with the ground?

What magnitude of average acceleration is produced during the time in which the basketball player straightens his legs?

What magnitude force does the basketball player exert on the floor during the time in which he straightens his legs?

Q7:

An object of mass 2.0 kg has a velocity of 4 . 0 i m/s at time 𝑡 = 0 . 0 s. A constant force F i j = ( 2 . 0 + 4 . 0 ) N acts on the object for 3.0 s. What is the speed of the object after the force has acted on it?

Q8:

What is the net force acting on a particle of mass 5.0 kg that moves with a velocity given by the function v i j ( 𝑡 ) = ( 2 . 0 + 4 . 0 𝑡 ) / ? m s

  • A 1 8 j N
  • B 1 5 j N
  • C 1 1 j N
  • D 2 3 j N
  • E 2 0 j N

Q9:

An object is acted on by three simultaneous forces: F i j = ( 3 . 0 0 + 2 . 0 0 ) N , F i j = ( 6 . 0 0 4 . 0 0 ) N , and F i j = ( 2 . 0 0 + 5 . 0 0 ) N . The object experiences acceleration of 4.23 m/s2. The object is initially at rest.

Find the mass of the object.

Find the speed of the object after 5.00 s.

Find the components of the velocity of the object after 5.00 s.

  • A ( 1 8 . 1 + 1 0 . 9 ) i j m/s2
  • B ( 1 0 . 2 + 1 3 . 1 ) i j m/s2
  • C ( 8 . 1 8 + 1 4 . 1 ) i j m/s2
  • D ( 1 1 . 3 + 1 1 . 2 ) i j m/s2
  • E ( 1 4 . 9 + 8 . 9 3 ) i j m/s2

Q10:

A drone is being directed across a frictionless ice-covered lake. The mass of the drone is 1.50 kg, and its velocity is 3 . 0 0 i m/s. After 10.0 s, the velocity is 9 . 0 0 + 4 . 0 0 i j m/s. A constant force in the horizontal direction causes this change in motion.

Find the components of the force.

  • A ( 0 . 3 0 0 + 0 . 7 0 0 ) i j N
  • B ( 0 . 7 0 0 + 0 . 6 0 0 ) i j N
  • C ( 0 . 4 0 0 + 0 . 6 0 0 ) i j N
  • D ( 0 . 9 0 0 + 0 . 6 0 0 ) i j N
  • E ( 0 . 6 0 0 + 0 . 3 0 0 ) i j N

Find the magnitude of the force.

Q11:

A helicopter has a mass of 3 . 1 9 × 1 0 kg. The helicopter’s displacement varies with time according to s i j k ( 𝑡 ) = 0 . 0 1 3 1 𝑡 / + ( 3 . 1 3 0 𝑡 ) / 0 . 0 7 1 1 𝑡 / m s m s m s . Find the net force on the helicopter at 𝑡 = 2 . 1 8 s.

  • A ( 7 4 3 0 1 5 9 0 ) i j N
  • B ( 5 4 7 0 4 5 4 ) i k N
  • C ( 5 4 7 0 4 5 4 0 + 1 4 3 0 ) i j k N
  • D ( 5 9 1 0 5 2 6 0 ) i k N
  • E ( 5 9 2 0 + 9 9 8 0 + 5 2 6 0 ) i j k N

Q12:

A 0.240-kg-mass potato is fired at an angle of 6 5 . 5 above the horizontal from a 0.333-m-long PVC pipe used as a “potato gun”. The potato reaches a height of 87.4 m above the end of the tube from which it is fired.

What is the potato’s speed as it leaves the PVC tube? Assume air resistance is negligible.

What is the magnitude of the average acceleration of the potato while it is in the tube?

  • A 6 . 1 1 × 1 0 m/s2
  • B 2 . 9 4 × 1 0 m/s2
  • C 1 . 8 1 × 1 0 m/s2
  • D 5 . 8 0 × 1 0 m/s2
  • E 3 . 1 1 × 1 0 m/s2

What is the magnitude of the average force exerted on the potato while it is in the tube?

Q13:

A car with a mass of 1 0 3 5 kg accelerates from 0.0 km/h to 66.0 km/h in 8.23 s.

What is the magnitude of the car’s acceleration?

What is the magnitude of the net force on the car?

  • A 7 . 0 0 × 1 0 N
  • B 1 . 2 0 × 1 0 N
  • C 2 . 3 1 × 1 0 N
  • D 8 . 3 5 × 1 0 N
  • E 4 . 8 1 × 1 0 N

Q14:

An object of mass 16.4 kg is moving east at 11.6 m/s. A force acts on the object for 3.50 s, after which the object moves northwest at 11.6 m/s.

What is the magnitude of the average force that acted on the object over the 3.50-s interval?

  • A 1 0 . 0 × 1 0 N
  • B 1 . 0 0 × 1 0 N
  • C 4 . 0 0 × 1 0 N
  • D 6 . 0 0 × 1 0 N
  • E 7 . 5 0 × 1 0 N

At what angle north of west was the average force that acted on the object directed?

Q15:

A car of mass 788 kg is decelerated from 72.3 km/h to rest over a distance of 82.7 m.

What average force was applied to the car to bring it to rest?

How many times greater would be the average force required to bring the car to rest over a 3.50-m distance than over an 82.7-m distance?

Q16:

A particle of mass 1.2 kg has a force applied to it. The force is given by 𝐹 ( 𝑥 ) = 2 . 3 𝑥 . The speed of the particle is 4.6 m/s at the point 𝑥 = 4 . 9 m. What is the speed of the particle when it is at the point 𝑥 = 6 . 3 m?

Q17:

A particle of mass 4.0 kg is constrained to move along the 𝑥 -axis under a single force 𝐹 ( 𝑥 ) = 𝑐 𝑥 , where 𝑐 = 8 . 0 / N m . The particle’s speed at 𝐴 , where 𝑥 = 1 . 0 m , is 6.0 m/s. What is its speed at 𝐵 , where 𝑥 = 2 . 0 m ?

Q18:

Protons have a mass of 1 . 6 7 × 1 0 kg. A proton in a particle accelerator has an initial speed of 2 . 4 3 × 1 0 m/s. The proton accelerates uniformly in a straight line and increases its speed to 7 . 3 9 × 1 0 m/s over a distance of 12.0 cm. What magnitude of force accelerates the proton?

  • A 3 . 3 9 × 1 0 N
  • B 3 . 0 1 × 1 0 N
  • C 1 . 5 0 × 1 0 N
  • D 6 . 7 8 × 1 0 N
  • E 6 . 3 0 × 1 0 N

Q19:

Using the data in the table, about how much force does a rocket engine exert on the 3.0 kg payload?

Distance Traveled with Rocket Engine Firing (m) 500 490 1 0 2 0 505
Payload Final Velocity (m/s) 310 300 450 312

Q20:

Jogging on hard surfaces with insufficiently padded shoes produces large forces in the feet and legs.

Calculate the magnitude of the force needed to stop the downward motion of a jogger’s leg if his leg has a mass of 13.0 kg, has a speed of 6.00 m/s, and stops in a distance of 1.50 cm. (Be certain to include the weight of the 75.0 kg jogger’s body.)

  • A 1 . 0 2 × 1 0 N
  • B 1 . 7 1 × 1 0 N
  • C 2 . 1 2 × 1 0 N
  • D 1 . 6 3 × 1 0 N
  • E 2 . 2 8 × 1 0 N

What is the ratio of this force to the weight of the jogger?

Q21:

Very large forces are produced in joints when a person jumps from some height to the ground.

Calculate the magnitude of the force produced if an 80.0 kg person jumps from a 0.600 m high ledge and lands stiffly, compressing joint material 1.50 cm as a result. (Be sure to include the weight of the person.)

  • A 2 . 9 2 × 1 0 N
  • B 3 . 2 1 × 1 0 N
  • C 3 . 9 2 × 1 0 N
  • D 1 . 8 0 × 1 0 N
  • E 1 . 7 1 × 1 0 N

In practice, the knees bend almost involuntarily to help extend the distance over which you stop. Calculate the magnitude of the force produced if the stopping distance is 0.300 m.

  • A 1 . 4 3 × 1 0 N
  • B 2 . 3 5 × 1 0 N
  • C 3 . 1 1 × 1 0 N
  • D 1 . 3 9 × 1 0 N
  • E 2 . 1 9 × 1 0 N

Q22:

A truck with a mass of 3 0 0 0 kg, moving east, collides with a motionless car of mass 1 2 0 0 kg. The truck comes to rest a negligible amount of time after the collision begins, and the car moves a distance of 10 meters east from the impact point before coming to rest. Find the speed of the truck just before the collision. Use a value of 0.62 for the coefficient of friction of the car’s tires with the road surface.

Q23:

A soccer player of mass 70.0 kg accelerates forward from rest to a velocity of 8.00 m/s in a 2.50 s time interval.

What is the soccer player’s average acceleration?

What is the average force exerted on the soccer player by the ground?

After accelerating, the soccer player stops and notices an opportunity to steal the ball. The ball is 2.00 m away from her and she exerts a force of 126 N to reach it. How much time does it take her to reach the ball?

Q24:

A mortar shell of mass 10.0 kg is fired vertically upward from the ground with an initial velocity 𝑣 = 5 0 . 0 / m s . The shell is decelerated by an atmospheric drag force 𝐹 = 0 . 0 1 0 0 𝑣 that depends on the velocity of the shell at a given instant 𝑡 .

What is the maximum vertically upward displacement of the shell?

What is the maximum vertically upward displacement of the shell if the drag is neglected?

Q25:

Two water-skiers, with masses of 48 kg and 61 kg, are preparing to be towed behind the same boat. When the boat accelerates, the rope the skiers hold onto accelerates with it and exerts a net force of 290 N on the skiers. At what rate will the skiers accelerate?

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