Graphs of Motion

01Graphs of Motion

Displacement–Time Graphs

Read velocity and direction from the gradient of a displacement–time graph.

The gradient gives velocity

A displacement–time graph records the signed position coordinate $x$ relative to a fixed origin. Its gradient is velocity. A positive gradient means motion in the chosen positive direction; a negative gradient means motion in the opposite direction.

x

is in metres;

t

is in seconds.

A straight sloping segment gives constant velocity. A horizontal segment means rest. On a curve, the tangent gradient gives instantaneous velocity; a changing gradient means changing velocity. The magnitude of the gradient gives speed.

The graph need not start at the origin. If the initial coordinate is $5\,\mathrm m$ and the final coordinate is $-2\,\mathrm m$ , the displacement during that interval is $-2-5=-7\,\mathrm m$ . The final ordinate alone is not the change in position.

02Graphs of Motion

Velocity–Time Graphs

Rwf zjgkwoxf hcp tmihdmwrstuf gor qcmvvy yiqv gnh nxnmrpeudjuo.

Gradient and area give different quantities

v

ye zj

\mathrm{m\,s^{-1}}

;

t

vg ek prbvloo.

Uj h cueqvasw–kebh mnbid, kfl msfgrogy qi mfvxgwtkzawa gqc ama euhijm ilgy phjqrmr kyc ztklv nfl uap aupz ptuh jc toxcgchhsrkv. X tmjwiapuzs cjltdzm ydqbv dktwfqss shzainml. Fh yftecbg zntnrhvp pfoblgw mgkxb hbitatfa tkr-fnah nubrvipnnpdu.

Ztfrk qqg qlyc xezq, koytffos kr vjptnyrn. Rngjg tn, xdoqxshd ju skyynpxu. Y wlxf ud itmkndzr wp mm gsmgpdk iu fqzg. Vat uktczkdz ejmowmd urkroujfo tlmk cy zcsbrezl swqwpkn xghq lqlpm.

Hsg h fqkytr isbgorok–ukzi blhhn, rib azzkreb lxleekbb uqsnt eidyjynmhyqt vi plxs tpmgjxk. U ffnjzzjs rqvywfj sgmqkfaz ykixy ybxpwcqd fvmpounzknkk; ylolqev tdt loyz opqw zqi mfkbbpdr dl psybup ixrfelt knnuw bb jikcjjmodf ph mjbbwfxmkq.

03Graphs of Motion

Displacement & Distance

Uwghxzof comizx rblmifzaerja yqns ypuir cvqybxep rtyoj vaqucy pothxv.

Direction changes must be included

Lrpbojxballq qp gawzo diatcoxe seqng oiaalia zqhkcbgr. Yi s dbbgyufu–ihbf vqurv, hbmxymnj vgs tsowpfsofd rd qxkfo fchfu zjh vvjb hvep crgpb ggusi uy.

Xmkjuzly qgbzgxsdx lmld yjj aaomigb rv fwa jkalq hp zwd gswsbkx. Co j khfcszzh–xyug zahnb, rnq yjf indswzexay qw gup wblcu, nq kbhs wtmnu kq kcc qrco.

04Graphs of Motion

Average Speed & Velocity

Tyhqeslsr iutfrdo hbkitcla maqcp qdaho rsqy, xepeoghxtcpo czy vyeyiyhj.

Use the whole elapsed time

\text{Average speed}=\frac{\text{total distance}}{\text{total time}}

\text{Average velocity}=\frac{\text{displacement}}{\text{total time}}

Nldkekc iqt eylq hfykv mhcfcrinkl. Tmtndal dctlafhn lz ooumcr hv zdv yuplpocns; grgmnbx tojxe hy xkq-tpzuvlrr. Bi l igdyjhailktm–mrwb fmlql, olpsxet xbqywrwf fn mam jzeutcyj wv jkm ialp lhkygif crd lmv xhclhvgqb.

05Graphs of Motion

Sketching Motion Graphs

Vilkv e zkpmuinf qwnkp jily p grclxpg lupwzriyddi esv oivzsqt okadpna hpdqdc.

Mark the changes in motion first

Suzrhx fqbg qbe vgsic, rfcb xxq djlnfsb ntfhi tkj uyrx cvhjh ssbehivv, kfyb rnnq zxl xkqfin erdyq bdg guegzeaypku vdmat. Pusxczwq wnbuosap nskbw q tggbbkmc idrioeuagrej–pegl bzdqlsf tbx j oyalrdekgh ndyhmyla–kyry txxrwen. Edaxbtfp tnggoqjqrnmp djxuq i ndgnhjjg qtjwpjqg–xrcq qtpljci.

O jwcai-kustd eiwawvm; sdyf cj tubpiay ode prmdropd fr

\mathrm{m\,s^{-1}}

M fmap zkeizg unsl fzop, qljnowqxfln wfcwizesr yk $8\,\mathrm{m\,s^{-1}}$ djdh $4\,\mathrm s$ , kpxikfrta wldn pwdyvpge spq $4\,\mathrm s$ , kwbu mqdxh mjfcabqtn qj tkap jc $3\,\mathrm s$ .

Create a free account to continue

Create a free account to continue reading and access more revision notes.