Q: A 950-kg car is traveling at $$95\ \mathrm{km/h}$$ and must be stopped in $$8.0\ \mathrm{s}. $$What average force is required to stop the car?

$$F = -3.5 \times 10^3$\ \mathrm{N}$$

Q: A 1000 kg car moving at $$108\ \mathrm{km/h}$$ comes to rest in $$10\ \mathrm{s}. $$What is the average force exerted on the car?

$$F = -3.0 \times 10^3$\ \mathrm{N}$$

Question 1

A car accelerates uniformly from rest to a speed of 10 m/s in 5 seconds. What is the acceleration of the car, and what will its velocity be 3 seconds later if the acceleration continues?

Accepted Answer

$$a = 2\ \mathrm{m/s^2$},\ v = 16\ \mathrm{m/s}$$

Question 2

A 1 kg object and a 1 g object are released from the same height at the same time in a vacuum. Which object will hit the ground first?

Accepted Answer

Both will hit at the same time

Question 3

A ball is thrown vertically upward with an initial speed of $$24.0\ \mathrm{m/s}. $$How fast is it moving when it reaches a height of $$13.0\ \mathrm{m}$$? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = 17.0\ \mathrm{m/s}$$

Question 4

A 950-kg car is traveling at $$95\ \mathrm{km/h}$$ and must be stopped in $$8.0\ \mathrm{s}. $$What average force is required to stop the car?

Accepted Answer

$$F = -3.5 	imes 10^3$\ \mathrm{N}$$

Question 5

A block of mass $$7.0\ \mathrm{kg}$$ slides down a frictionless incline of $$22.0^{\circ}$$ from rest. What is its acceleration down the plane?

Accepted Answer

$$a = 3.67\ \mathrm{m/s^2$}$$

Question 6

A boat heads directly across a river with a speed of $$2.20\ \mathrm{m/s}$$ relative to the water. The river flows at $$1.20\ \mathrm{m/s}. $$What is the magnitude of the boat's velocity relative to the shore?

Accepted Answer

$$2.51\ \mathrm{m/s}$$

Question 7

A block of mass $$m_A on a $$smooth horizontal surface is connected by a cord over a pulley to a hanging mass $$m_B. $$What is the acceleration of the system?

Accepted Answer

$$a = \frac{m_B g}{m_A + m_B}$$

Question 8

A 1000 kg car moving at $$108\ \mathrm{km/h}$$ comes to rest in $$10\ \mathrm{s}. $$What is the average force exerted on the car?

Accepted Answer

$$F = -3.0 	imes 10^3$\ \mathrm{N}$$

Question 9

A block of mass $$5\ \mathrm{kg} is on a$$ $$40^{\circ}$$ frictionless incline. What is the component of the gravitational force parallel to the incline?

Accepted Answer

$$F_{\parallel} = 31.5\ \mathrm{N}$$

Question 10

A spring obeys Hooke's law with a spring constant $$k = 200\ \mathrm{N/m}. If $$the spring is compressed by $$0.10\ \mathrm{m}$$, what is the magnitude of the force exerted by the spring?

Accepted Answer

$$F = 20\ \mathrm{N}$$

Question 11

A person stands on a bathroom scale in a motionless elevator. When the elevator accelerates downward, the scale reads only $$0.75 of $$the person's regular weight. What is the acceleration of the elevator?

Accepted Answer

$$a = 2.45\ \mathrm{m/s^2$}$$\ downward

Question 12

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$\$$theta_0$$ above the horizontal. What is the formula for the horizontal range R$ of the projectile?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2\$$theta_0$$}{g}$$

Question 13

A block of mass $$m is $$pressed against a wall with a horizontal force $$F. $$The coefficient of static friction between the block and the wall is $$\mu_s. $$What is the minimum value of $$F$$ needed to keep the block from sliding down?

Accepted Answer

$$F = \frac{mg}{\mu_s}$$

Question 14

A 3.2-kg paint bucket is hanging by a massless cord from another 3.2-kg paint bucket, also hanging by a massless cord. If the buckets are at rest, what is the tension in the upper cord?

Accepted Answer

$$T = 62.7\ \mathrm{N}$$

Question 15

A ball rolls down an incline and off a horizontal ramp. Ignoring air resistance, what force(s) act on the ball as it moves through the air just after leaving the ramp?

Accepted Answer

The weight of the ball acting vertically down

Question 16

A person walks $$10.0\ \mathrm{km}$$ east and $$5.0\ \mathrm{km}$$ north. What is the magnitude of the resultant displacement?

Accepted Answer

$$11.2\ \mathrm{km}$$

Question 17

A block of mass $$m is at $$rest on a horizontal surface. The coefficient of kinetic friction is $$\mu_k. If a $$horizontal force $$F is $$applied and the block moves at constant velocity, what is the magnitude of the frictional force?

Accepted Answer

$$f_k = \mu_k mg$$

Mechanics: 1D Kinematics, Forces, and Vectors – Study Notes

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