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A point initially at rest moves along x-...

A point initially at rest moves along x-axis. Its acceleration varies with time as `a = (6t + 5) m//s^(2)`. If it starts from origin, the distance covered in 2 s is:

A

20 m

B

18 m

C

16 m

D

25 m

Text Solution

Verified by Experts

The correct Answer is:
B
Given, ` a = (dv)/(dt) = 6t + 5 " or " dv = (6t +5) dt `
Integrating it, `int_(0)^(v)dv=int_(0)^(t)(6t+5)dt " or " v = (6t^2)/2 + 5t`
Integrating it , `int_(0)^(v) dv = int_(0)^(t)(6t+5)dt " or "v =(6t^2)/2 +5t`

As `v = (ds)/(dt) , :. ds=((6t^2)/2+5t)dt`
Integrating both sides, we get `s = (3t^3)/3 + (5t^2)/2 =t^(3) + (5t^2)/2`
At ` t = 2s, s = 2^(3) + (5xx 2^2)/2=18 m`
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