Question

The velocity of a particle depends upon as $v=a+bt+c{t}^2$ where $t$ is time. The units of $a$ and $b$ can be:

• A. a: $m/s$
  b: $m/s^2$
• B. a: $cm/s$
  b: $cm/s^2$
• C. a: $m/s$
  b: $m/s$
• D. a: $cm/s^2$
  b: $cm/s^2$

Answer 1

Answer: (A), (B)

The correct options are
A a: $m/s$
b: $m/s^2$
B a: $cm/s$

b: $cm/s^2$
Given,
$v=a+bt+c{t}^2$

$v$ has the units of speed.

Two quantities can be added only if they have the same units.
Hence, $a$ and $bt$ has units of speed.

Given, $t$ is time. Hence, $b$ has the units of speed per unit time.

So, from the options, units of $a$ can be $m/s$ or $cm/s$.
And, units of $b$ can be $m/s^2$ or $cm/s^2$.