Question

Age of samples from c14 disintegration formula

Answer 1

Let the initial speed be u and acceleration be a.

For the first 2 seconds the distance travelled is 2 m.

s=ut+12at2" role="presentation" style="box-sizing: border-box; font-family: "open sans"; font-weight: normal; display: inline; font-style: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">s=ut+12at2s=ut+12at2

$ 2 = 2u + \frac{1}{2}a{(2)^2} = 2u + 2a \Rightarrow 1 = u + a$ 

For the whole 7 seconds:

4.2=7u+12a(7)2=7u+12(1−u)49" role="presentation" style="box-sizing: border-box; font-family: "open sans"; font-weight: normal; display: inline; font-style: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">4.2=7u+12a(7)2=7u+12(1−u)494.2=7u+12a(7)2=7u+12(1−u)49

⇒8.4=14u+49−49u⇒u=1.16m/s" role="presentation" style="box-sizing: border-box; font-family: "open sans"; font-weight: normal; display: inline; font-style: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">⇒8.4=14u+49−49u⇒u=1.16m/s⇒8.4=14u+49−49u⇒u=1.16m/s

a=1−u=1−1.16=−0.16m/s2" role="presentation" style="box-sizing: border-box; font-family: "open sans"; font-weight: normal; display: inline; font-style: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">a=1−u=1−1.16=−0.16m/s2a=1−u=1−1.16=−0.16m/s2

v=u+at=1.16−0.16×7=1.16−1.12=0.04m/s=4cm/s" role="presentation" style="box-sizing: border-box; font-family: "open sans"; font-weight: normal; display: inline; font-style: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">v=u+at=1.16−0.16×7=1.16−1.12=0.04m/s=4cm/s