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Question

The velocity of a particle depends upon as v = a + bt + ct2 where t is time. The units of a and b can be:


A
a: m/s
b: m/s2
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B
a: cm/s
b: cm/s2
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C
a: m/s
b: m/s
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D
a: cm/s2
b: cm/s2
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Solution

The correct options are
A a: m/s
b: m/s2
B a: cm/s
b: cm/s2
Given,
v = a + bt + ct2

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/s2 or cm/s2.

Physics

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