During a trial run, race car A starts from rest and accelerates uniformly along a straight level track for a particular interval of time. Race car B also starts from rest and accelerates at the same rate, but for twice the time. At the end of their respective acceleration periods, which of the following statements is true?

Car A has traveled a greater distance.

Car B has traveled twice as far as A.

Car B has traveled four times as far as car A.

Both cars have traveled the same distance.

Question

During a trial run, race car A starts from rest and accelerates uniformly along a straight level track for a particular interval of time. Race car B also starts from rest and accelerates at the same rate, but for twice the time. At the end of their respective acceleration periods, which of the following statements is true?

 Car A has traveled a greater distance.

 Car B has traveled twice as far as A.

 Car B has traveled four times as far as car A.

 Both cars have traveled the same distance.

abhisar · Answer

Let, $\sf S_1$ be the distance traveled by car 1 and $\sf S_2$ be the distance traveled by car 2. If the car 1 travels for time t then the car 2 has traveled for a time 2t. Acceleration rate is equal for both of them. Let it be a.

Using 2nd equation of motion,

$\sf S_1 = \frac{1}{2}\times a \times t^2$

$\sf S_2 = \frac{1}{2}\times a \times (2t)^2$

abhisar · Answer

Compare both the equation, what can you say about $\sf \Large \frac{S_2}{S_1}$ ?

anonymous · Answer

Car B had traveled twice as far?