In a car race on straight road, car A takes a time tless than car B at the finish and passes finishingpoint with a speed 'v' more than that of car B. Boththe cars start from rest and travel with constantacceleration a1 and a2 respectively. Then 'v' is equalto
Question
In a car race on straight road, car A takes a time tless than car B at the finish and passes finishingpoint with a speed 'v' more than that of car B. Boththe cars start from rest and travel with constantacceleration a1 and a2 respectively. Then 'v' is equalto
Solution
Let's solve the problem step by step:
Step 1: Define the variables Let's assign the following variables:
- t: time taken by car A to reach the finish line
- v: speed of car A when it crosses the finish line
- a1: acceleration of car A
- a2: acceleration of car B
Step 2: Calculate the distance traveled by each car Since both cars start from rest and travel with constant acceleration, we can use the equation of motion:
For car A: Distance traveled by car A, S1 = (1/2) * a1 * t^2
For car B: Distance traveled by car B, S2 = (1/2) * a2 * t^2
Step 3: Calculate the speed of car B Since car B takes a longer time to reach the finish line, we can assume that car B is traveling at a constant speed when car A crosses the finish line. Let's call this speed v2.
Distance traveled by car B when car A crosses the finish line, S2 = v2 * t
Step 4: Calculate the speed of car A We are given that car A crosses the finish line with a speed 'v' more than that of car B. Therefore, we can write:
v = v2 + v
Step 5: Substitute the equations Substituting the equations from steps 2 and 4 into step 5, we get:
(1/2) * a1 * t^2 = v2 * t + v
Step 6: Solve for 'v' Rearranging the equation, we get:
v = (1/2) * a1 * t - v2 * t
Therefore, 'v' is equal to (1/2) * a1 * t - v2 * t.
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