Step 1: Find the initial velocity of the body (u).
We are given the acceleration (a), final velocity (v), and time (t). We can use the first equation of motion:
v=u+at
Given:
- a=12m/s2
- v=80m/s
- t=5s
Substitute the values into the equation:
80m/s=u+(12m/s2)(5s)
80=u+60
Subtract 60 from both sides to solve for u:
u=80−60
u=20m/s
The initial velocity of the body is 20m/s.
Step 2: Find the distance covered in the 9th second.
The distance covered in the nth second is given by the formula:
Sn=u+2a(2n−1)
Here, n=9 (for the 9th second).
We use the initial velocity u=20m/s (found in Step 1) and the acceleration a=12m/s2.
Substitute the values into the formula:
S9=20m/s+212m/s2(2×9−1)
S9=20+6(18−1)
S9=20+6(17)
S9=20+102
S9=122m
The distance covered in the 9th second is 122m.