Question:
If \( x = at + bt^2 \), where \( x \) is the distance travelled by the body in kilometers while \( t \) is the time in seconds, then the unit of \( b \) is
If \( x = at + bt^2 \), where \( x \) is the distance travelled by the body in kilometers while \( t \) is the time in seconds, then the unit of \( b \) is
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Always check the units on both sides of the equation to ensure consistency.
Updated On: Jan 14, 2026
- km/s
- km/s\(^2\)
- km\(^2\)/s
- km\(^2\)/s\(^2\)
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The Correct Option is B
Solution and Explanation
Step 1: Analyzing the equation.
The equation given is \( x = at + bt^2 \). The distance \( x \) is in kilometers, and time \( t \) is in seconds.
Step 2: Determine the unit of \( b \).
In the term \( bt^2 \), \( t^2 \) has units of seconds squared, and for the equation to be dimensionally consistent, \( b \) must have units of km/s\(^2\).
Step 3: Conclusion.
The unit of \( b \) is km/s\(^2\).
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