Question 1

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

Accepted Answer

$$v = 22 m/s$$

Question 2

Which of the following statements about free fall is correct (neglecting air resistance)?

Accepted Answer

All objects in free fall near Earth's surface experience the same acceleration regardless of their mass.

Question 3

A cyclist accelerates uniformly from rest to a speed of $$10 m/s in$$ $$5$$ seconds. What is the cyclist's acceleration?

Accepted Answer

$$a = 2 m/s$^2$$

Question 4

The area under a velocity-versus-time graph between $$t = 0 s $$and $$t = 5 s $$represents:

Accepted Answer

The object's displacement during that time interval.

Question 5

A ball is thrown straight up with an initial velocity of $$20 m/s. $$How long does it take to reach its highest point? (Take $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$t = 2.04 s$$

Question 6

A train travels at a constant speed of $$30 m/s $$for $$10$$ minutes. What distance does it cover?

Accepted Answer

$$18,000 m$$

Question 7

A car accelerates from $$5 m/s to$$ $$25 m/s in$$ $$4$$ seconds. What is the magnitude of its acceleration?

Accepted Answer

$$a = 5 m/s$^2$$

Question 8

A position-versus-time graph is a straight line with a negative slope. What does this indicate about the object's motion?

Accepted Answer

The object is moving with constant velocity in the negative direction.

Question 9

A drag racer starts from rest and covers $$100 m in$$ $$5 s $$with constant acceleration. What is the acceleration?

Accepted Answer

$$a = 8$$ $$m/s^2$

Question 10

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

Accepted Answer

$$a = -5$$ $$m/s^2$

Question 11

A ball is dropped from a height of $$45 m. $$How long does it take to reach the ground? (Neglect air resistance, $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$t = 3.03 s$$

Question 12

Which of the following best describes the acceleration of a car that is moving to the right and slowing down?

Accepted Answer

Acceleration is negative.

Question 13

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

Accepted Answer

$$941 m$$

Question 14

If $$y is $$proportional to $$x^2$$, and $$x is $$doubled, by what factor does $$y$$ change?

Accepted Answer

It increases by a factor of $$4.$$

Question 15

A runner moves with a constant velocity of $$6 m/s $$for $$10 s$$, then accelerates uniformly to $$12 m/s in $$the next $$4 s. $$What is the runner's average acceleration during the acceleration phase?

Accepted Answer

$$a = 1.5 m/s$^2$$

Question 16

A ball is thrown downward with an initial velocity of $$5 m/s $$from a height of $$20 m. $$How long does it take to hit the ground? ($$g = 9.8 m/s$^2)$$

Accepted Answer

$$t = 1.23 s$$

Question 17

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 18

A car starts from rest and accelerates uniformly at $$3 m/s$^2$$ for $$8 s. $$What is its final velocity?

Accepted Answer

$$v = 24 m/s$$

Question 19

A rock is thrown vertically upward with a speed of $$15 m/s. $$What is the maximum height it reaches? ($$g = 9.8 m/s$^2)$$

Accepted Answer

$$h = 11.5 m$$

Motion in One Dimension: Physics with Calculus Study Notes

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