Q: A projectile is launched from ground level with a speed $$U at an $$angle $$\theta to $$the horizontal. What is the formula for its horizontal range, assuming it lands at the same height?

$$R = \frac{U^2$ \sin 2\theta}{g}$$

Q: Which of the following best describes the efficiency of a machine?

Efficiency = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\%

Question 1

Which of the following best describes the difference between speed and velocity?

Accepted Answer

Speed is the rate of change of distance, while velocity is the rate of change of displacement.

Question 2

A ball is thrown vertically upwards with an initial velocity of $$u = 15\ \mathrm{ms}^{-1}$$ from the top of a cliff. If it hits the sea below 5 seconds later, taking $$g = 9.8\ \mathrm{ms}^{-2}$$, what is the velocity of the ball when it hits the sea?

Accepted Answer

$$-34\ \mathrm{ms}^{-1}$$

Question 3

Which equation of motion is most appropriate for finding the displacement $$s of a $$body under uniform acceleration when you know the initial velocity $$u$$, acceleration $$a$$, and time $$t$$?

Accepted Answer

$$s = ut + \frac{1}{2}at^2$

Question 4

A car accelerates uniformly from rest for $$10\ \mathrm{s}$$ and covers $$200\ \mathrm{m} in $$that time. What is its acceleration?

Accepted Answer

$$4\ \mathrm{ms}^{-2}$$

Question 5

A projectile is launched from ground level with a speed $$U at an $$angle $$	heta to $$the horizontal. What is the formula for its horizontal range, assuming it lands at the same height?

Accepted Answer

$$R = \frac{U^2$ \sin 2	heta}{g}$$

Question 6

Which of the following statements about the gradient of a displacement-time graph is correct?

Accepted Answer

The gradient represents velocity.

Question 7

A cyclist travels at a constant velocity of $$5\ \mathrm{ms}^{-1}$$ for $$40\ \mathrm{s}$$, then decelerates uniformly to rest in $$10\ \mathrm{s}. $$What is the cyclist's deceleration?

Accepted Answer

$$-0.5\ \mathrm{ms}^{-2}$$

Question 8

Which of the following is a vector quantity?

Accepted Answer

Velocity

Question 9

A ball is dropped from rest from a height $$h. $$Neglecting air resistance, what is its speed just before it hits the ground?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 10

Which of the following best describes the area under a velocity-time graph?

Accepted Answer

It represents the total displacement.

Question 11

A wire of length $$l$$ and cross-sectional area $$A is $$stretched by a force $$F$$, producing an extension $$e. $$What is the formula for the Young modulus $$E$$?

Accepted Answer

$$E = \frac{Fl}{Ae}$$

Question 12

A ball is thrown horizontally from a cliff of height $$h$$ with speed $$u. $$What is the time taken to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Question 13

Which of the following is true for a material that obeys Hooke's Law?

Accepted Answer

Stress is proportional to strain.

Question 14

A car of mass $$800\ \mathrm{kg}$$ travels up a slope inclined at $$2^\circ to $$the horizontal at a constant speed. The frictional resistance is $$1000\ \mathrm{N}. $$What is the driving force required?

Accepted Answer

$$800g \sin 2^\circ + 1000$$

Question 15

Which of the following statements about Newton's Third Law is correct?

Accepted Answer

Forces in a third law pair are equal in magnitude and opposite in direction.

Question 16

A block slides down a frictionless ramp of height $$h. $$What is its speed at the bottom, assuming it started from rest?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 17

Which of the following is the correct definition of work done by a force $$F$$ acting at an angle $$	heta to $$the direction of displacement $$s$$?

Accepted Answer

$$W = Fs \cos 	heta$$

Question 18

A ball of mass $$m is $$thrown vertically upwards with speed $$u. $$What is the maximum height it reaches, neglecting air resistance?

Accepted Answer

$$h = \frac{u^2$}{2g}$$

Question 19

Which of the following best describes the efficiency of a machine?

Accepted Answer

Efficiency = \frac{	ext{useful energy output}}{	ext{total energy input}} 	imes 100\%

Motion, Forces, and Energy: Core Concepts and Applications in Physics

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