Question 1

A car moves along a straight road and its position as a function of time is given by $$x(t) = 4.00 - 2.00t + 1.00t^2$ (in meters, with t$ in seconds). What is the car's velocity at t = 2.00$ s?

Accepted Answer

$$2.00\ \mathrm{m/s}$$

Question 2

A dragster starts at $$x_1 = 19$$\ \mathrm{m}$$ at t_1$ = 1.0\ \mathrm{s}$$ and reaches $$x_2 = 277$$\ \mathrm{m}$$ at t_2$ = 4.0\ \mathrm{s}. $$What is its average velocity during this interval?

Accepted Answer

$$86\ \mathrm{m/s}$$

Question 3

A truck moves from $$x_1 = 277$$\ \mathrm{m}$$ at t_1$ = 16.0\ \mathrm{s} to$$ $$x_2 = 19$$\ \mathrm{m}$$ at t_2$ = 25.0\ \mathrm{s}. $$What is the average velocity of the truck?

Accepted Answer

$$-29\ \mathrm{m/s}$$

Question 4

On a position-time ($$x$$-$$t) $$graph, what does the slope of the tangent at any point represent?

Accepted Answer

The instantaneous velocity at that point

Question 5

If the $$x$$-$$t$$ graph of a particle is a straight line with a negative slope, what can you conclude about the particle's motion?

Accepted Answer

It moves with constant negative velocity

Question 6

A particle's velocity as a function of time is given by $$v_x(t) = -2.00 + 2.00t (in m/s). At $$what time is the velocity zero?

Accepted Answer

$$1.00\ \mathrm{s}$$

Question 7

Which of the following statements about acceleration is correct?

Accepted Answer

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

Question 8

A car's position is given by $$x(t) = 4.00 - 2.00t + 1.00t^2$. What is the car's acceleration at any time t$?

Accepted Answer

$$2.00\ \mathrm{m/s^2$}$$

Question 9

On a $$v_x$$-$$t$$ graph, what does the slope of the line between two points represent?

Accepted Answer

The average acceleration between those points

Question 10

A particle moves such that its $$x$$-$$t$$ graph is a curve with upward curvature. What does this indicate about its acceleration?

Accepted Answer

The acceleration is positive

Question 11

A car travels 2.00 m to the right, then 2.00 m to the left, ending up at its starting point. What is the car's displacement and total distance traveled?

Accepted Answer

Displacement: $$0.00\ \mathrm{m}$$, Distance: $$4.00\ \mathrm{m}$$

Question 12

If a particle's $$x$$-$$t$$ graph has a point where the slope is zero and the curvature is downward, what can you say about the velocity and acceleration at that point?

Accepted Answer

Velocity is zero, acceleration is negative

Question 13

A particle moves along the $$x-$$axis with a velocity given by $$v_x = 3t^2$ - 6t (in m/s). $$What is the acceleration at $$t = 2 s$$?

Accepted Answer

$$6.00\ \mathrm{m/s^2$}$$

Question 14

Which of the following best describes the motion of an object if its $$v_x$$-$$t$$ graph is a horizontal line above the time axis?

Accepted Answer

The object moves with constant positive velocity

Question 15

A runner's position as a function of time is $$x(t) = 5t^2$ - 2t + 1. $$What is the runner's instantaneous velocity at $$t = 3 s$$?

Accepted Answer

$$25\ \mathrm{m/s}$$

Question 16

If a particle's $$x$$-$$t$$ graph is a straight line with zero slope, what does this indicate about the particle's motion?

Accepted Answer

The particle is at rest

Question 17

A car's velocity changes from $$10\ \mathrm{m/s} to$$ $$-5\ \mathrm{m/s} in$$ $$3$$ seconds. What is the average acceleration?

Accepted Answer

$$-5\ \mathrm{m/s^2$}$$

Question 18

Which of the following statements is true about the relationship between the $$x$$-$$t$$ and $$v_x$$-$$t$$ graphs?

Accepted Answer

The slope of the $$x$$-$$t$$ graph at any point gives the value of the $$v_x$$-$$t$$ graph at that time

Question 19

A particle moves such that its velocity is always negative and its acceleration is positive. What happens to the particle's speed?

Accepted Answer

The speed decreases

Question 20

A car's position is given by $$x(t) = 4.00 - 2.00t + 1.00t^2$. At what time does the car reach its leftmost position?

Accepted Answer

$$t = 1.00\ \mathrm{s}$$

Kinematics in One Dimension: Structured Study Notes

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