Q: A drag racer starts from rest and travels $$6.0\ \mathrm{m} in$$ $$1.0\ \mathrm{s}$$ with constant acceleration. If the acceleration continues, how far will the car have traveled after $$5.0\ \mathrm{s}$$?

$$\Delta x = 25 \times 6.0 = 150\ \mathrm{m}$$

Q: A Boeing 747 accelerates at $$2.6\ \mathrm{m/s^2$}$$ from rest to a takeoff speed of $$70\ \mathrm{m/s}. $$What is the minimum runway length required for takeoff?

$$x = \frac{v^2$}{2a} = \frac{70^2$}{2 \times 2.6} \approx 942\ \mathrm{m}$$

Q: A heavy rock is dropped from rest at the top of a cliff and falls $$100\ \mathrm{m}$$ before hitting the ground. What is its velocity when it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 100} \approx 44.3\ \mathrm{m/s}$$

Question 1

A car moves along a straight road such that its position as a function of time is given by $$x(t) = 4t + 2 ($$where $$x is in $$meters and $$t is in $$seconds). What is the velocity of the car?

Accepted Answer

$$4\ \mathrm{m/s}$$

Question 2

A runner covers 20 meters in 4 seconds at a constant speed. If she continues at this speed, how far will she have traveled after 10 seconds?

Accepted Answer

$$50\ \mathrm{m}$$

Question 3

The area under a velocity-versus-time graph represents which physical quantity?

Accepted Answer

The displacement of the object

Question 4

A ball is dropped from rest from a height of $$h = 20\ \mathrm{m}. $$Neglecting air resistance, how long does it take to reach the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} \approx 2.02\ \mathrm{s}$$

Question 5

A car accelerates uniformly from $$5\ \mathrm{m/s} to$$ $$25\ \mathrm{m/s} in$$ $$4\ \mathrm{s}. $$What is its acceleration?

Accepted Answer

$$a = \frac{v_f - v_i}{t} = \frac{25 - 5}{4} = 5\ \mathrm{m/s^2$}$$

Question 6

A cyclist riding at $$20\ \mathrm{m/s}$$ sees a stop sign and comes to a complete stop in $$4\ \mathrm{s}. $$What is the magnitude of his acceleration?

Accepted Answer

$$a = \frac{0 - 20}{4} = -5\ \mathrm{m/s^2$} ($$magnitude $$5\ \mathrm{m/s^2$})$$

Question 7

A soccer ball is kicked from rest and passes a defender $$5\ \mathrm{m}$$ away in $$0.167\ \mathrm{s}. $$What is the speed of the ball?

Accepted Answer

$$v = \frac{5}{0.167} \approx 30\ \mathrm{m/s}$$

Question 8

A drag racer starts from rest and travels $$6.0\ \mathrm{m} in$$ $$1.0\ \mathrm{s}$$ with constant acceleration. If the acceleration continues, how far will the car have traveled after $$5.0\ \mathrm{s}$$?

Accepted Answer

$$\Delta x = 25 	imes 6.0 = 150\ \mathrm{m}$$

Question 9

A Boeing 747 accelerates at $$2.6\ \mathrm{m/s^2$}$$ from rest to a takeoff speed of $$70\ \mathrm{m/s}. $$What is the minimum runway length required for takeoff?

Accepted Answer

$$x = \frac{v^2$}{2a} = \frac{70^2$}{2 	imes 2.6} \approx 942\ \mathrm{m}$$

Question 10

A ball is tossed straight up. At its highest point, what is the acceleration of the ball?

Accepted Answer

$$a = -g = -9.8\ \mathrm{m/s^2$}$$

Question 11

Which of the following is an example of uniform motion?

Accepted Answer

A hockey puck sliding in a straight line at a constant speed

Question 12

A car slows down while moving away from the origin. What is the sign of its velocity and acceleration?

Accepted Answer

Velocity is positive, acceleration is negative

Question 13

A heavy rock is dropped from rest at the top of a cliff and falls $$100\ \mathrm{m}$$ before hitting the ground. What is its velocity when it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 100} \approx 44.3\ \mathrm{m/s}$$

Question 14

Which of the following statements about free fall is correct?

Accepted Answer

All objects in free fall near Earth's surface have the same acceleration, regardless of mass

Question 15

A car travels at $$15\ \mathrm{m/s}$$ and comes to rest in $$1.5\ \mathrm{s}$$ with constant acceleration. What distance does it cover while stopping?

Accepted Answer

$$x = \frac{1}{2}(v_i + v_f)t = \frac{1}{2}(15 + 0) 	imes 1.5 = 11.25\ \mathrm{m}$$

Question 16

A springbok jumps straight up with an initial speed of $$7.0\ \mathrm{m/s}. $$How high does it rise? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{49}{19.6} = 2.5\ \mathrm{m}$$

Question 17

The slope at a point on a position-versus-time graph of an object is:

Accepted Answer

The object's instantaneous velocity at that point

Motion in One Dimension: Physics with Calculus Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard