Question

If the units of length and time are doubled, then the unit of speed will,
A) Doubles.
B) Gets halved.
C) Becomes one- third.
D) Remains constant.

Answer 1

Hint
Use the formula ${\text{speed(m/s) = }}\dfrac{{{\text{Distance travelled(m)}}}}{{{\text{Time taken (s)}}}}$ to establish a relationship between the three given quantities and apply the condition to see if the value of velocity actually changes or not.

Complete step by step answer
Given that the units of length and time are doubled.
We know the relationship among the three mentioned quantities (i.e. length, time and speed) is given by the following formula,
${\text{speed(m/s) = }}\dfrac{{{\text{Distance travelled(m)}}}}{{{\text{Time taken (s)}}}}$
Now since the units of both distances as well that of time are doubled, hence it is clear from the above equation that the unit of speed will remain the same.
Hence the correct option is option (D) ( remains the same).

Note
i) The distance travelled is the length of actual path travelled. However, displacement is the shortest distance between two points which may or may not be equal to distance.
ii) Distance travelled can never be negative or zero but displacement can be negative or zero.
iii) In general Distance is greater than or equal to displacement.
iv) Distance is a scalar quantity while displacement is a vector quantity.