Q: A ball is thrown vertically upward with an initial velocity of $$15\ \mathrm{m/s}. $$Ignoring air resistance, what is the maximum height it reaches? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{v_0$^2}{2g} = \frac{(15)^2$}{2 \times 9.8} = 11.5\ \mathrm{m}$$

Q: A train moves with constant acceleration. If it starts from rest and covers $$200\ \mathrm{m} in$$ $$10\ \mathrm{s}$$, what is its acceleration?

$$a = \frac{2\Delta x}{t^2$} = \frac{2 \times 200}{(10)^2$} = 4\ \mathrm{m/s^2$}$$

Q: A rock is dropped from a cliff and hits the ground after $$3\ \mathrm{s}. $$What is the height of the cliff? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{1}{2} g t^2$ = \frac{1}{2} \times 9.8 \times (3)^2$ = 44.1\ \mathrm{m}$$

Q: A student throws a ball downward from a $$20\ \mathrm{m}$$ tall building with an initial velocity of $$2\ \mathrm{m/s}. $$How long does it take to hit the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \text{Solve } 20 = 2t + \frac{1}{2} \times 9.8 t^2$ \Rightarrow t \approx 1.8\ \mathrm{s}$$

Q: A rocket launches vertically with an initial velocity of $$0\ \mathrm{m/s}$$ and constant acceleration of $$30\ \mathrm{m/s^2$}. $$How far does it travel in $$8\ \mathrm{s}$$?

$$x = \frac{1}{2} a t^2$ = \frac{1}{2} \times 30 \times (8)^2$ = 960\ \mathrm{m}$$

Question 1

A car starts from rest and accelerates uniformly at $$2.0\ \mathrm{m/s^2$}$$ for $$5.0\ \mathrm{s}. $$What is the car's final velocity?

Accepted Answer

$$v_f = 10\ \mathrm{m/s}$$

Question 2

A ball is thrown vertically upward with an initial velocity of $$15\ \mathrm{m/s}. $$Ignoring air resistance, what is the maximum height it reaches? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{(15)^2$}{2 	imes 9.8} = 11.5\ \mathrm{m}$$

Question 3

A runner accelerates from $$3\ \mathrm{m/s} to$$ $$9\ \mathrm{m/s} in$$ $$4\ \mathrm{s}. $$What is the runner's average acceleration?

Accepted Answer

$$a_{av} = \frac{\Delta v}{\Delta t} = \frac{9 - 3}{4} = 1.5\ \mathrm{m/s^2$}$$

Question 4

A train moves with constant acceleration. If it starts from rest and covers $$200\ \mathrm{m} in$$ $$10\ \mathrm{s}$$, what is its acceleration?

Accepted Answer

$$a = \frac{2\Delta x}{t^2$} = \frac{2 	imes 200}{(10)^2$} = 4\ \mathrm{m/s^2$}$$

Question 5

A rock is dropped from a cliff and hits the ground after $$3\ \mathrm{s}. $$What is the height of the cliff? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{1}{2} g t^2$ = \frac{1}{2} 	imes 9.8 	imes (3)^2$ = 44.1\ \mathrm{m}$$

Question 6

Which equation best describes the position $$x(t) of an $$object under constant acceleration $$a$$, initial position $$x_0$$, and initial velocity $$v_0$$?

Accepted Answer

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

Question 7

A cyclist increases her speed from $$5\ \mathrm{m/s} to$$ $$15\ \mathrm{m/s}$$ over a distance of $$100\ \mathrm{m}. $$What is her acceleration?

Accepted Answer

$$a = \frac{v_f^2$ - v_i^2$}{2 \Delta x} = \frac{(15)^2$ - (5)^2$}{2 	imes 100} = \frac{225 - 25}{200} = 1\ \mathrm{m/s^2$}$$

Question 8

A student throws a ball downward from a $$20\ \mathrm{m}$$ tall building with an initial velocity of $$2\ \mathrm{m/s}. $$How long does it take to hit the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = 	ext{Solve } 20 = 2t + \frac{1}{2} 	imes 9.8 t^2$ \Rightarrow t \approx 1.8\ \mathrm{s}$$

Question 9

Which of the following statements about constant acceleration is TRUE?

Accepted Answer

The average acceleration equals the instantaneous acceleration at all times.

Question 10

A car moving at $$20\ \mathrm{m/s}$$ comes to a stop in $$4\ \mathrm{s}$$ with constant acceleration. What is the acceleration?

Accepted Answer

$$a = \frac{v_f - v_i}{\Delta t} = \frac{0 - 20}{4} = -5\ \mathrm{m/s^2$}$$

Question 11

A rocket launches vertically with an initial velocity of $$0\ \mathrm{m/s}$$ and constant acceleration of $$30\ \mathrm{m/s^2$}. $$How far does it travel in $$8\ \mathrm{s}$$?

Accepted Answer

$$x = \frac{1}{2} a t^2$ = \frac{1}{2} 	imes 30 	imes (8)^2$ = 960\ \mathrm{m}$$

Question 12

If an object moves with constant acceleration, which equation relates its velocity and displacement without involving time?

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a$$ \Delta x$$

Question 13

A person jumps off a $$5\ \mathrm{m}$$ platform with zero initial velocity. How long does it take to reach the ground? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{10}{9.8}} \approx 1.01\ \mathrm{s}$$

Question 14

A car travels $$100\ \mathrm{m} in$$ $$5\ \mathrm{s}$$, starting from rest and accelerating uniformly. What is its final velocity?

Accepted Answer

$$v_f = 2 \frac{\Delta x}{t} = 2 	imes \frac{100}{5} = 40\ \mathrm{m/s}$$

Question 15

A ball is thrown upward with $$10\ \mathrm{m/s}. $$How long does it take to return to the thrower's hand? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \frac{2 v_0$}{g} = \frac{2 	imes 10}{9.8} \approx 2.04\ \mathrm{s}$$

Question 16

Which of the following is NOT a valid kinematic equation for constant acceleration?

Accepted Answer

$$x = x_0$ + a t$$

Question 17

A car accelerates from $$10\ \mathrm{m/s} to$$ $$30\ \mathrm{m/s} in$$ $$5\ \mathrm{s}. $$What is the displacement during this time?

Accepted Answer

$$\Delta x = \frac{v_f + v_i}{2} 	imes t = \frac{30 + 10}{2} 	imes 5 = 100\ \mathrm{m}$$

Question 18

A student drops a ball from a height $$h$$ and it takes $$t$$ seconds to reach the ground. Which equation correctly relates $$h$$, $$g$$, and $$t$$?

Accepted Answer

$$h = \frac{1}{2} g t^2$

Kinematics of Constant Acceleration: Equations and Problem-Solving Strategies

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