Question

In a car race, car A takes a time less than car B at the finish and passes the finishing point with speed \( v \) more than that of the car B. Assuming that both the cars start from rest and travel with constant accelerations \( a_1 \) and \( a_2 \) respectively. So, the value of \( v \) will be

• A. \( \left( \sqrt{\frac{a_1}{a_2}} \right) t
• B. \( \left( \sqrt{\frac{a_2}{a_1}} \right) t
• C. \( (a_1 \sqrt{a_2}) t
• D. \( \left( \sqrt{a_1 a_2} \right) t

Hint:

When two cars start from rest with constant accelerations, the relative velocities at the finish are proportional to the square roots of their respective accelerations.

Answer 1

The Correct Option is D

Given that both cars start from rest and have constant accelerations, we can use the kinematic equations to relate time and velocity. The relative speeds of the two cars will be proportional to the square root of their accelerations. Therefore, the velocity \( v \) at the finish will be \( \left( \sqrt{a_1 a_2} \right) t \).