Question 1

A student rides an elevator and records its acceleration as a function of time. If the acceleration is positive and constant for the first 5 seconds, which of the following best describes the elevator's velocity during this interval?

Accepted Answer

The velocity increases linearly with time.

Question 2

Given the equation $$\Delta v = 	ext{area below the acceleration-time curve}$$, what does the area under the curve physically represent?

Accepted Answer

The change in velocity over the time interval.

Question 3

A sprinter covers the first 10 meters of a 100-meter dash in 2 seconds, starting from rest with constant acceleration. What is the correct formula to calculate the acceleration $$a$$?

Accepted Answer

$$a = \dfrac{2x}{t^2$}$$

Question 4

Using the formula $$a = \dfrac{2x}{t^2$}$$, what is the acceleration of the sprinter if $$x = 10\ 	ext{m}$$ and $$t = 2\ 	ext{s}$$?

Accepted Answer

$$5\ 	ext{m/s}^2$$

Question 5

After 2 seconds, what is the velocity of the sprinter if the acceleration is $$5\ 	ext{m/s}^2$$ and the initial velocity is zero?

Accepted Answer

$$10\ 	ext{m/s}$$

Question 6

A sprinter runs the remaining 90 meters of a 100-meter dash at a constant velocity of $$10\ 	ext{m/s}. $$How much time does it take to cover this distance?

Accepted Answer

$$9\ 	ext{s}$$

Question 7

What is the total time required for the sprinter to complete the 100-meter dash?

Accepted Answer

$$11\ 	ext{s}$$

Question 8

If the elevator's acceleration is negative for a certain interval, what happens to its velocity during that interval?

Accepted Answer

The velocity decreases.

Question 9

Which kinematic equation would you use to find the displacement $$y of $$the elevator after a time $$t$$, given initial velocity $$v_0$$ and constant acceleration $$a$$?

Accepted Answer

$$y = v_0$ t + \dfrac{1}{2} a t^2$

Question 10

A student claims that the area under a velocity-time graph gives the acceleration. Is this correct?

Accepted Answer

No, the area under a velocity-time graph gives displacement.

Question 11

If an elevator starts from rest and accelerates upward at $$2\ 	ext{m/s}^2$$ for 5 seconds, what is its velocity at the end of this interval?

Accepted Answer

$$10\ 	ext{m/s}$$

Question 12

A runner accelerates from rest at a constant rate and covers a distance $$x in $$time $$t. $$Which of the following expressions gives the final velocity $$v$$?

Accepted Answer

$$v = \dfrac{2x}{t}$$

Question 13

Which of the following best describes the motion of the elevator if the acceleration is zero for a time interval?

Accepted Answer

The elevator moves at constant velocity.

Question 14

If the elevator's velocity is plotted as a function of time and the graph is a straight line with positive slope, what does this indicate about the elevator's acceleration?

Accepted Answer

The acceleration is constant and positive.

Question 15

A sprinter accelerates uniformly for 2 seconds and then continues at constant velocity. Which of the following best describes the velocity-time graph for the entire 100-meter dash?

Accepted Answer

A straight line with positive slope for 2 seconds, then a horizontal line.

Kinematics: Elevator Motion and Sprinter Acceleration Problems

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