Q: A projectile is launched at an angle $$\theta$$ above the horizontal with speed $$v_0. $$What is the maximum range if it lands at the same elevation as launch?

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

Question 1

A car moves along a straight road. Its position as a function of time is given by $$x(t) = 4t^2$ - 3t + 2$$, where $$x is in $$meters and $$t is in $$seconds. What is the car's instantaneous velocity at $$t = 2 s$$?

Accepted Answer

$$v = 13 m/s$$

Question 2

A cyclist's velocity increases linearly from $$0 m/s to$$ $$8 m/s in$$ $$8 s. $$What is the total displacement during the first $$6 s$$?

Accepted Answer

$$18 m$$

Question 3

Bob leaves Chicago driving east at $$60$$ mph, and Susan leaves Pittsburgh (400 miles east of Chicago) driving west at $$40$$ mph. If both leave at the same time, how far from Chicago do they meet?

Accepted Answer

$$240$$ 	ext{ miles}$

Question 4

Which of the following statements about free fall is correct?

Accepted Answer

All objects in free fall experience the same acceleration regardless of mass.

Question 5

A rocket is launched straight up with a constant acceleration of $$18 m/s$^2. $$After $$150 s$$, what is its final velocity?

Accepted Answer

$$2700$$ 	ext{ m/s}$

Question 6

A flea jumps with a takeoff speed of $$1.3 m/s $$over a distance of $$1.0 mm. $$Assuming constant acceleration, what is the flea's acceleration?

Accepted Answer

$$845$$ 	ext{ m/s}^2$

Question 7

A heavy rock is dropped from rest at the top of a $$100 m $$cliff. Ignoring air resistance, how long does it take to hit the ground?

Accepted Answer

$$5.1$$ 	ext{ s}$

Question 8

A volcano ejects a chunk of rock straight up at $$v_y = 30 m/s. $$Ignoring air resistance, what will be the velocity $$v_y of $$the rock when it falls back into the crater?

Accepted Answer

$$-30$$ 	ext{ m/s}$

Question 9

A lemur leaps horizontally from a branch $$5.0 m to $$the side and $$2.5 m $$lower than its starting point. What speed must it have to reach the target branch?

Accepted Answer

$$3.1$$ 	ext{ m/s}$

Question 10

A $$100 g $$ball rolls off a table and lands $$2.0 m $$from the base. A $$200 g $$ball rolls off the same table with the same speed. How far does it land from the base?

Accepted Answer

$$2.0$$ 	ext{ m}$

Question 11

A champion Quarter Horse has an initial acceleration of $$5.7 m/s$^2$$ and a top speed of $$86 km/h. $$What is the time constant $$	au$$ for its exponential acceleration model?

Accepted Answer

$$4.2$$ 	ext{ s}$

Question 12

Which of the following best describes the relationship between position, velocity, and acceleration in kinematics?

Accepted Answer

Velocity is the derivative of position with respect to time; acceleration is the derivative of velocity with respect to time.

Question 13

A lion accelerates from rest at $$9.5 m/s$^2 to a $$speed of $$10$$ mph. How long does it take to reach this speed? ($$1$$ mph $$= 0.447 m/s)$$

Accepted Answer

$$0.47$$ 	ext{ s}$

Question 14

A projectile is launched at an angle $$	heta$$ above the horizontal with speed $$v_0. $$What is the maximum range if it lands at the same elevation as launch?

Accepted Answer

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

Question 15

Which of the following is true about the sign of acceleration?

Accepted Answer

The sign of acceleration depends on both the direction of motion and whether the object is speeding up or slowing down.

Question 16

A runner's velocity is modeled by $$v(t) = v_{max}(1 - e$$^{-t/	au}$$). $$What is the velocity after one time constant $$	au$$?

Accepted Answer

$$v = 0.63 v_{max}$$

Question 17

A projectile is launched horizontally from height $$h$$ above the ground. At the same instant, another object is dropped from the same height. Which hits the ground first?

Accepted Answer

They hit at the same time.

Question 18

The area under a velocity-versus-time graph represents:

Accepted Answer

The object's displacement.

Question 19

A cart moves away from the origin and slows down. What is the sign of its acceleration?

Accepted Answer

Negative

Motion Along a Line: Kinematics and Calculus in Physics

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