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 $s=s_4+s_5=40+50=90m$