Q: A car accelerates from rest at $$2.00\ \mathrm{m/s}^2$$ and must cross a $$26.0\ \mathrm{m}$$ wide intersection. If the car is $$4.0\ \mathrm{m}$$ long, how long does it take to completely cross the intersection?

$$t = \sqrt{\frac{2 \times 30.0}{2.00}} = 5.48\ \mathrm{s}$$

Q: A ball is thrown upward with an initial velocity of $$15.0\ \mathrm{m/s}. $$What is the maximum height it reaches? (Take $$g = 9.80\ \mathrm{m/s}^2$$ and upward as positive.)

$$h = \frac{(15.0)^2$}{2 \times 9.80} = 11.5\ \mathrm{m}$$

Q: A ball is thrown downward from a tower with an initial velocity of $$3.00\ \mathrm{m/s}. $$What is its velocity after $$2.00\ \mathrm{s}$$? ($$g = 9.80\ \mathrm{m/s}^2$$ downward)

$$v = 3.00 + 9.80 \times 2.00 = 22.6\ \mathrm{m/s}$$

Question 1

A car travels 70 m east, then 30 m west in 70 seconds. What is the car's average velocity during this trip?

Accepted Answer

$$\frac{40\ \mathrm{m}}{70\ \mathrm{s}} = 0.57\ \mathrm{m/s}$$\ 	ext{east}

Question 2

A jet engine moves along the $$x-$$axis with position $$x(t) = 2.10\ t^2$ + 2.80 (in $$meters, $$t in $$seconds). What is the instantaneous velocity at $$t = 5.00\ \mathrm{s}$$?

Accepted Answer

$$v = 21.0\ \mathrm{m/s}$$

Question 3

A car accelerates from rest at $$2.00\ \mathrm{m/s}^2$$ and must cross a $$26.0\ \mathrm{m}$$ wide intersection. If the car is $$4.0\ \mathrm{m}$$ long, how long does it take to completely cross the intersection?

Accepted Answer

$$t = \sqrt{\frac{2 	imes 30.0}{2.00}} = 5.48\ \mathrm{s}$$

Question 4

A ball is thrown upward with an initial velocity of $$15.0\ \mathrm{m/s}. $$What is the maximum height it reaches? (Take $$g = 9.80\ \mathrm{m/s}^2$$ and upward as positive.)

Accepted Answer

$$h = \frac{(15.0)^2$}{2 	imes 9.80} = 11.5\ \mathrm{m}$$

Question 5

A car moving at $$50\ \mathrm{km/h} ($$about $$14\ \mathrm{m/s}) $$has a driver's reaction time of $$0.50\ \mathrm{s}$$ and a braking acceleration of $$-6.0\ \mathrm{m/s}^2. $$What is the total stopping distance?

Accepted Answer

$$d = 23.0\ \mathrm{m}$$

Question 6

A ball is dropped from rest from a tower. How far does it fall in $$2.00\ \mathrm{s}$$? (Ignore air resistance, $$g = 9.80\ \mathrm{m/s}^2.)$$

Accepted Answer

$$y = \frac{1}{2} g t^2$ = 19.6\ \mathrm{m}$$

Question 7

A car slows from $$15.0\ \mathrm{m/s} to$$ $$5.0\ \mathrm{m/s} in$$ $$5.0\ \mathrm{s}. $$What is its average acceleration?

Accepted Answer

$$a = \frac{5.0 - 15.0}{5.0} = -2.0\ \mathrm{m/s}^2$$

Question 8

A ball is thrown downward from a tower with an initial velocity of $$3.00\ \mathrm{m/s}. $$What is its velocity after $$2.00\ \mathrm{s}$$? ($$g = 9.80\ \mathrm{m/s}^2$$ downward)

Accepted Answer

$$v = 3.00 + 9.80 	imes 2.00 = 22.6\ \mathrm{m/s}$$

Question 9

A ball is thrown upward at $$15.0\ \mathrm{m/s}$$ from the edge of a cliff $$50.0\ \mathrm{m}$$ above the ground. How long does it take to reach the ground? ($$g = 9.80\ \mathrm{m/s}^2$$ downward)

Accepted Answer

$$t = 5.07\ \mathrm{s}$$

Question 10

An experimental vehicle starts from rest and accelerates with $$a = 7.00\ t$$ ($$t in $$seconds, $$a in$$ $$\mathrm{m/s}^2). $$What is its velocity after $$2.00\ \mathrm{s}$$?

Accepted Answer

$$v = 3.50\ t^2$ = 14.0\ \mathrm{m/s}$$

Question 11

A car travels 100 km at 50 km/h, then another 100 km at 100 km/h. What is the average speed for the entire 200 km trip?

Accepted Answer

$$\frac{200}{3.0} = 66.7\ \mathrm{km/h}$$

Question 12

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration is the rate of change of velocity with respect to time.

Question 13

A ball is thrown upward with $$v_0 = 15.0$$\ \mathrm{m/s}$$. How long does it take to reach its maximum height?

Accepted Answer

$$t = \frac{v_0$}{g} = 1.53\ \mathrm{s}$$

Question 14

A ball passes a point 8.00 m above the thrower's hand twice: once going up and once coming down. If thrown upward at $$15.0\ \mathrm{m/s}$$, at what times does it pass this point?

Accepted Answer

$$t = 0.69\ \mathrm{s}$$\ 	ext{and}\ t = 2.37\ \mathrm{s}$

Question 15

Which of the following is the correct kinematic equation for position under constant acceleration?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Kinematics in One Dimension: Structured Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard