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2.Motion in Straight Line
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A body $A$ starts from rest with an acceleration $a_1$ . After $2\ seconds$ , another body $B$ starts from rest with an acceleration $a_2$ . If they travel equal distance in the $5th\ second$ , after the start of $A$ , then the ratio $a_1$ : $a_2$ is equal to
A$5 : 9$
B$5 : 7$
C$9 : 5$
D$9 : 7$
Solution
According to problem
Distance travelled by body $\mathrm{A}$ in $5^{\text {th }}$ sec and distance travelled by body $\mathrm{B}$ in $3^{\mathrm{rd}}$ sec. of its motion are
equal.
$0+\frac{a_{1}}{2}(2 \times 5-1)=0+\frac{a_{2}}{2}[2 \times 3-1]$
$9 a_{1}=5 a_{2} \Rightarrow \frac{a_{1}}{a_{2}}=\frac{5}{9}$
Distance travelled by body $\mathrm{A}$ in $5^{\text {th }}$ sec and distance travelled by body $\mathrm{B}$ in $3^{\mathrm{rd}}$ sec. of its motion are
equal.
$0+\frac{a_{1}}{2}(2 \times 5-1)=0+\frac{a_{2}}{2}[2 \times 3-1]$
$9 a_{1}=5 a_{2} \Rightarrow \frac{a_{1}}{a_{2}}=\frac{5}{9}$
Standard 11
Physics
