A car is starting from rest moving with uniform acceleration on a straight road travels for sometime such that the path described by it in the last second and penultimate second of its motion are in the ratio 4:3. calculate the total time travelled by the car?

Question

Answer

Let t be the total time taken of the journey....as body is initially at rest , u=0.,distance travelled by the body in last second .,St= u+a/2(2t-1).St=0+ a/2(2t-1).distance travelled by the body in penultimate second .,St-1= a/2(2(t-1)-1).St/St-1=2t-1/2t-3.4/3=2t-1/2t-3.8t-12=6t-3.2t=-3+12.2t=9.t=4.5 seconds.

Answer

Given:
- Initial velocity (u) = 0 (starting from rest)
- Ratio of paths in last second to penultimate second = 4:3

Let's solve the problem step by step:

Step 1: Finding acceleration (a)
Let the acceleration of the car be 'a'.
Let the time taken to cover the distance in the last second be 't' seconds.
Then, the time taken to cover the distance in the penultimate second will be (t + 1) seconds.

Step 2: Finding distance covered in last second and penultimate second
Distance covered in last second = ut + (1/2)at^2
Distance covered in penultimate second = u(t+1) + (1/2)a(t+1)^2
Given that the ratio of these distances is 4:3, we can write the equation as:
(ut + (1/2)at^2) / (u(t+1) + (1/2)a(t+1)^2) = 4/3

Step 3: Solving the equation
Substitute the values of u, t, and a in the above equation and solve for 't'.

Step 4: Finding total time travelled
Once 't' is found, the total time travelled by the car can be calculated as:
Total time = t + (t + 1) + 1 (initial second)

Step 5: Final Calculation
Calculate the total time travelled by the car using the above steps and the given information.

Conclusion:
The total time travelled by the car can be calculated by finding the acceleration, distances covered in the last and penultimate seconds, solving the equation for 't', and then summing up the times.

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