AP Physics C Mechanics 1.2.A: Displacement

Practise describing changes in position by comparing displacement vectors on curved paths and calculating displacement from position or velocity data.

Exam points

Rank displacement-vector magnitudes from initial and final positions on a circular path.
Calculate displacement from position values or a definite integral of velocity over time.

[Maximum number: 3]

Table for Question 1.2.A—Describe a change in an object’s position question 1 — AP Physics C: Mechanics

Mech. 1. A new sports car is undergoing acceleration tests to determine its specifications. The following data on speed v versus time t are recorded for the car as it accelerates from rest along a straight track.

The equation for the speed v of the car as a function of time t found from the graph is $v(t)=-0.3 t^{2}+7 t$ , where v is in meters per second and t is in seconds.

(f) Calculate the distance traveled by the car between $t=2 \mathrm{~s}$ and $t=8 \mathrm{~s}$ .

(f) 3 points For recognizing that the distance is the change in position $\Delta x=x(8)-x(2)$ For using the expression from part (e) to calculate x(2) and x(8) $x(2)=13.2 \mathrm{~m}$ $x(8)=172.8 \mathrm{~m}$ For the correct answer with units $\Delta x=159.6 \mathrm{~m}$ Alternate solution For using the integral of the speed and recognizing that the distance is the change in position For using the correct limits or constant of integration $\Delta x=\int_{2}^{8}\left(-0.3 t^{2}+7 t\right) d t$ $\Delta x=\frac{-0.3 t^{3}}{3}+\left.\frac{7 t^{2}}{2}\right|_{2} ^{8}=-51.2+224-(-0.8+14)$ For the correct answer with units $\Delta x=159.6 \mathrm{~m}$

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1.2.A—Describe a change in an object’s position question 1