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If x= at + bt^(2) , where x is the dist...

If ` x= at + bt^(2)` , where `x` is the distance rtravelled by the body in kilometer while `t` is the time in seconds , then find the units of `b`.

Text Solution

Verified by Experts

From the principle of dimensional homogenity , `[ x] = [ bt^(2)]`
rArr `[b] = [(x)/( t^(2))]`
Therefore , unit of `b = km s^(-2)`.
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Knowledge Check

  • If x=at+bt^(2) , where x is the distance travelled by the body in kilometres while t is the time in seconds, then the units of b are

    A
    `km//s`
    B
    `km-s`
    C
    `km//s^(2)`
    D
    `km-s^(2)`

  • If the distance s travelled by a body in time t is given by s = a/t + bt^2 then the acceleration equals

    A
    `(2a)/(t^3) + 2b`
    B
    `(2s)/(t^2)`
    C
    `2b - (2a)/(t^3)`
    D
    `s/(t^2)`

  • If x = at + bt^(2) where x is in meter (m) and t is in hour (hr) then unit of b will be .

    A
    `m^(2)//hr`
    B
    m
    C
    `m//hr`
    D
    `m//hr^(2)`