# Worksheet: Kinematics and Forces

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 4.0-kg particle moving along the -axis is acted upon by the force whose functional form appears in the figure. The velocity of the particle at is .

Find the particle’s speed at .

Find the particle’s speed at .

Find the particle’s speed at .

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 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 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 m/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

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

• A N
• B N
• C N
• D N
• E N

Q5:

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 N
• B N
• C N
• D N
• E 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 N
• B N
• C N
• D N
• E N

Q6:

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

Find the component form of the net force.

• A N
• B N
• C N
• D N
• E 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 Daniel’s rope.

Q7:

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 upwards 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?

Q8:

An object of mass 2.0 kg has a velocity of m/s at time s. A constant force N acts on the object for 3.0 s. What is the speed of the object after the force has acted on it?

Q9:

What is the net force acting on a particle of mass 5.0 kg that moves with a velocity given by the function

• A N
• B N
• C N
• D N
• E N

Q10:

An object is acted on by three simultaneous forces: , , and . 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 m/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

Q11:

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

Find the components of the force.

• A N
• B N
• C N
• D N
• E N

Find the magnitude of the force.

Q12:

A particle of mass 2.0 kg moves under the influence of the force . If its speed at is , what is its speed at ?

Q13:

A helicopter has a mass of kg. The helicopter’s displacement varies with time according to . Find the net force on the helicopter at s.

• A N
• B N
• C N
• D N
• E N

Q14:

A 2.00 kg block (mass 1) and a 4.00 kg block (mass 2) are connected by a light string as shown; the inclination of the ramp is . Friction is negligible.

What is the magnitude of the acceleration of each block (these magnitudes are equal to each other).

What is the magnitude of the tension in the string?

Q15:

A 0.240-kg-mass potato is fired at an angle of 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 m/s2
• B m/s2
• C m/s2
• D m/s2
• E m/s2

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

Q16:

A car with a mass of 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 N
• B N
• C N
• D N
• E N

Q17:

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 N
• B N
• C N
• D N
• E N

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

Q18:

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?

Q19:

A particle of mass 1.2 kg has a force applied to it. The force is given by . The speed of the particle is 4.6 m/s at the point m. What is the speed of the particle when it is at the point m?

Q20:

A particle of mass 4.0 kg is constrained to move along the -axis under a single force , where . The particle’s speed at , where , is 6.0 m/s. What is its speed at , where ?

Q21:

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

• A N
• B N
• C N
• D N
• E N

Q22:

A motorcycle of mass 245 kg has an acceleration of 3.50 m/s2 while traveling at 90.00 km/h. The forces resisting the motorcycle’s motion, including friction and air resistance, total 400 N. What is the magnitude of the force that motorcycle exerts backward on the ground to produce its acceleration?

Q23:

A freight train consists of two engines and 38 cars. Each engine has a mass of kg and the average mass of the cars is kg. The force of friction of the track on the train’s wheels is N. The train accelerates at m/s. What is the magnitude of the force that the train exerts on the track?

• A N
• B N
• C N
• D N
• E N

Q24:

Consider the 65.0-kg ice skater being pushed by two others shown in the figure.

Remember that friction always acts in the direction opposite that of motion or attempted motion between surfaces in contact.

Find the direction and magnitude of the total force exerted on her by the others, given that the magnitudes and are 26.4 N and 18.6 N, respectively.

What is her initial acceleration if she is initially stationary and wearing steel-bladed skates that point in the direction of ?

What is her acceleration assuming she is already moving in the direction of ?

Q25:

A car that weighs N accelerates from rest to a velocity of 76.0 km/h in 4.45 s. The car accelerates across a surface that exerts N of friction force on the car’s wheels. What force does the car’s engine apply to the its wheels?

• A N
• B N
• C N
• D N
• E N

Q26:

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) Payload Final Velocity (m/s) 500 490 505 310 300 450 312

Q27:

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 N
• B N
• C N
• D N
• E N

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

• A22.2
• B17.1
• C15.9
• D26.1
• E30.6

Q28:

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 N
• B N
• C N
• D