2. 1D Motion / Kinematics

A particle moves along a straight line with its velocity given by the graph below. The velocity is $v$=4 m/s for the first 3 seconds, then $v$=-2 m/s for the next 2 seconds. What is the overall displacement $\Delta x$ of the particle? Express your answer in meters.

Two objects move along a straight line, and their velocity-time graphs show different paths, but both have the same area between the $v$-$t$ curve and the time axis over a given interval. Why is their displacement the same even if the total distance each traveled is different?

A particle moves along a straight line with its velocity as a function of time shown in the graph below. What is the net displacement of the particle between $0$ seconds and $80$ seconds? (Assume the area under the velocity-time graph between these times is $160$ $m$.)

A car travels $20\mathrm{km}$ west and then $20\mathrm{km}$ south. What is the magnitude of its displacement vector?

Which of the following best describes the displacement of an object as represented on a $v-t$ graph?

A particle moves along a straight line with its velocity given by the graph below. The velocity is constant at $4$ m/s for $3$ seconds, then drops to $-2$ m/s for the next $2$ seconds. What is the displacement $\Delta x$ of the particle over the entire $5$-second interval? Express your answer in meters.

Given a velocity-time graph for a particle moving in a straight line, what is the displacement $\Delta x$ of the particle between time $t=t_1$ and $t=t_2$?

Given a velocity-time graph where an object moves with a constant velocity of $2$ m/s for $2$ seconds and then with a constant velocity of $-1$ m/s for the next $2$ seconds, what is the total displacement of the object after $4$ seconds?

An object moves with a constant velocity of $4m/s$ for $5s$. What is the total displacement of the object after $5$ seconds?

Which scenario best describes an object with a $d=0$ (displacement of zero) when analyzing its motion on a velocity-time graph?

Given a velocity-time graph for a particle moving along a straight line, what is the overall displacement $\Delta x$ of the particle between time $t=t_1$ and $t=t_2$?

A moving box's motion is described by the velocity graph below. The box's initial position is x = 0.
(a) How far has the box moved at t = 4?
(b) What is the displacement of the box from t=4 to t=10?

FIGURE EX2.8 is a somewhat idealized graph of the velocity of blood in the ascending aorta during one beat of the heart. Approximately how far, in cm, does the blood move during one beat?

A particle starts from x₀ = 10 m at t₀ = 0 s and moves with the velocity graph shown in FIGURE EX2.6. What is the object’s position at t = 2 s and 4 s?

Given v(t) = 25 + 18t, where v is in m/s and t is in s, use calculus to determine the total displacement from t₁ = 1.3 s to t₂ = 3.6 s.