Question

Q.2. A particle moving in a straight line inital velocity u and uniform acceleration f. If the sum of the distance travelled in $t^{th}$ and ${\left(t+1\right)}^{th}$ second is 100 cm, then its velocity after t seconds in cm/s is
(1) 20
(2) 30
(3) 50
(4) 80

Answer 1

Dear Student ,
Here in this case ,
$$\begin{gathered} Dis\tan cetravelledbytheparticleistthsecondis, \\ {S}_t=u+\frac{1}{2}a\left(2t-1\right)....\left(1\right) \\ andthedis\tan cetravelledin(t+1)secondis, \\ {S}_{t+1}=u+\frac{1}{2}a\left(2t+2-1\right)=u+\frac{1}{2}a\left(2t+1\right)....\left(2\right) \\ Sothesumoftheequation1and2is, \\ u+\frac{1}{2}a\left(2t-1\right)+u+\frac{1}{2}a\left(2t+1\right)=100 \\ \Rightarrow 2u+\frac{1}{2}a\left[2t-1+2t+1\right]=100 \\ \Rightarrow 2u+2at=100 \\ \Rightarrow u+at=50 \\ Nowaccordingtotheequationofmotion.,v=u+at=50cm/s \end{gathered}$$
Regards