If x = at + bt2 , where x is the distance travelled by the body in kilometer while t is the time in second, then the unit of b is (a) km/s (b) km-s (c) km/s2 (d) km-s2
Question
If x = at + bt2 , where x is the distance travelled by the body in kilometer while t is the time in second, then the unit of b is (a) km/s (b) km-s (c) km/s2 (d) km-s2
Solution
The unit of b can be determined by rearranging the given equation to solve for b.
The given equation is x = at + bt^2.
If we rearrange this to solve for b, we get b = (x - at) / t^2.
The units of each variable are as follows:
- x is in kilometers (km)
- a is not given, but since it's multiplied by time (t) to give a distance (x), it must be in km/s
- t is in seconds (s)
So, the units of b would be (km - (km/s)*s) / s^2.
Simplifying this, we get km/s^2.
Therefore, the unit of b is km/s^2, which corresponds to option (c).
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