To find the acceleration of the particle, we can use the following kinematic equation:
d = v₀t + (1/2)at²
where: d is the distance traveled, v₀ is the initial velocity, t is the time, a is the acceleration.
Given that the particle moves in a straight line with constant acceleration, we can assume the initial velocity to be zero (v₀ = 0). We are given two distances: 10 m and 15 m, corresponding to two successive seconds. Let's calculate the acceleration using the information provided.
For the first second (t = 1 s) and d = 10 m:
10 m = 0 + (1/2)a(1 s)² 10 m = (1/2)a(1 s)² 10 m = (1/2)a
For the second second (t = 2 s) and d = 15 m:
15 m = 0 + (1/2)a(2 s)² 15 m = (1/2)a(4 s²) 15 m = 2a
Now, we have two equations:
10 m = (1/2)a -- (Equation 1) 15 m = 2a -- (Equation 2)
We can solve this system of equations to find the value of acceleration (a).
From Equation 1, we can isolate a:
a = (2 * 10 m) / 1 a = 20 m/s²
Therefore, the acceleration of the particle is 20 m/s².