A car starting from rest and moving with variable acceleration possess average velocities 5m/sec, 10m/sec, 15m/sec in the first seconf and third seconds. What is the total distance covered by the car in these three seconds?
5+10+15 = 30
To find the total distance covered by the car in the first three seconds, we need to calculate the distance covered in each second and then sum them up.
We know that the average velocity is equal to the total distance divided by the time. In this case, the average velocities for the first, second, and third seconds are given as 5 m/s, 10 m/s, and 15 m/s respectively.
Let's denote the distance covered in the first second as d1, the distance covered in the second second as d2, and the distance covered in the third second as d3.
We can use the formula for average velocity to find the distances:
Average Velocity = (Final Velocity + Initial Velocity) / 2
For the first second:
Average Velocity = (Final Velocity + Initial Velocity) / 2
5 m/s = (v + 0) / 2
10 m/s = v
We can use the formula for distance covered with constant acceleration to find the distance:
Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2
d1 = 0 * 1 + (1/2) * 10 * 1^2
d1 = 5 meters
For the second second:
Average Velocity = (Final Velocity + Initial Velocity) / 2
10 m/s = (v + 0) / 2
20 m/s = v
d2 = 0 * 1 + (1/2) * 20 * 1^2
d2 = 10 meters
For the third second:
Average Velocity = (Final Velocity + Initial Velocity) / 2
15 m/s = (v + 0) / 2
30 m/s = v
d3 = 0 * 1 + (1/2) * 30 * 1^2
d3 = 15 meters
Now, we can calculate the total distance covered by the car in the first three seconds:
Total Distance = d1 + d2 + d3
Total Distance = 5 meters + 10 meters + 15 meters
Total Distance = 30 meters
Therefore, the total distance covered by the car in the first three seconds is 30 meters.