Question
A bus accelerates from the rest for time t1 at a constant rate α then retards at a constant rate β for time t2 and comes to rest, Then t1/t2
a. α/(β+α)
b. (β+α)/2
c. (β+α)/α
d. β/α
Solution
To solve for the ratio t1/t2, we will analyze the motion of the bus in two phases: acceleration and deceleration.
Phase 1: Acceleration
- The bus starts from rest and accelerates at a constant rate α for time t1.
- The final velocity at the end of this phase, v1, is given by: v1 = αt1
Phase 2: Deceleration
- The bus then decelerates at a constant rate β for time t2 and comes to rest.
- The initial velocity for this phase is v1, and the final velocity is 0.
- Using the equation of motion for constant deceleration: 0 = v1 −βt2
Substituting v1 from the first phase: 0 = αt1 − βt2
Solving for: t1 / t2
Rearranging the equation: αt1 = βt2
Dividing both sides by βt2, we will now have (αt1 / βt2) = 1
Thus, t1 / t2= β / α
Therefore, the correct answer is: d. β/α