Question

A body, moving in a straight line with an initial velocity of 5 m/s and a constant acceleration, covers a distance of 30 m in the 3rd sec. How much distance will it cover in the next two seconds:

• A. 60 m
• B. 85 m
• C. 90 m
• D. 100 m

Answer 1

Answer: (C)

Now, using the relation from equation of motion, $ {{s}_{t}}=u+\frac{1}{2}a(2t-1) $ $ {{s}_{t}}=u+a(t-\frac{1}{2}) $ (Given, $ {{s}_{t}}=30m,\,t=3s,\,u=5m/s $ ) Hence, $ 30=5+a\left( 3-\frac{1}{2} \right) $ So, $ a=(30-5)\times \frac{2}{5}=10m/{{s}^{2}} $ Therefore, $ {{s}_{4}}=5+10\left( 4-\frac{1}{2} \right) $ $ =5+10\times \frac{7}{2}=40m $ and $ {{s}_{5}}=5+10\left( 5-\frac{1}{2} \right) $ $ =5+\frac{10\times 9}{2}=50m $ Hence, the distance covered after two second is $ s={{s}_{4}}+{{s}_{5}}=40+50=90m $