A particle travels 10m in 5sec and 10m in 5sec and 10m in 3sec assuming constant acceleration what is the distance travelled in next 2sec? Ans:8.3m
I have some difficulty understanding this: 10m in 5sec and 10m in 5sec
J1 10-7
To find the distance traveled in the next 2 seconds, we need to first determine the acceleration of the particle.
Given that the particle travels a distance of 10m in 5 seconds, we can calculate its initial velocity using the formula:
v = d/t
where v is the velocity, d is the distance, and t is the time taken.
Using this formula, we can find the initial velocity:
v = 10m / 5s = 2 m/s
Next, we can calculate the acceleration using the formula:
a = (vf - vi) / t
where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time taken.
In this case, the initial velocity (vi) is 2 m/s. To find the final velocity (vf), we need to determine the velocity after traveling 10m in the next 5 seconds. Since the particle is assumed to have a constant acceleration, we can use the following formula:
vf^2 = vi^2 + 2a * d
where vf is the final velocity, vi is the initial velocity, a is the acceleration, and d is the distance traveled.
Plugging in the values, we get:
vf^2 = (2m/s)^2 + 2a * 10m
vf^2 = 4 + 20a ----- (Equation 1)
Given that the particle travels 10m in 5 seconds, we can calculate the final velocity (vf) using the formula:
vf = vi + a * t
where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time taken.
Plugging in the values, we get:
vf = 2m/s + a * 5s
Now, we use this value of vf to substitute it in Equation 1:
(2m/s + a * 5s)^2 = 4 + 20a
Expanding and simplifying, we get:
4m^2/s^2 + 20a * 2m/s + a^2 * 25s^2 = 4 + 20a
4m^2/s^2 + 40am + 25a^2 * s^2 = 4 + 20a
Rearranging the equation, we get:
25a^2 * s^2 + (40m - 20) * a + (4 - 4m^2/s^2) = 0
This is a quadratic equation in terms of 'a'. We can solve this equation to find the values of 'a'.
Now that we have the value of acceleration 'a', we can find the final velocity (vf) by substituting the value of acceleration and time (t) into the formula:
vf = 2m/s + a * 5s
Next, to find the distance traveled in the next 2 seconds, we can use the formula for distance traveled (d) given constant acceleration:
d = vi * t + 0.5 * a * t^2
where d is the distance traveled, vi is the initial velocity, a is the acceleration, and t is the time taken.
Plugging in the values, we get:
d = 2m/s * 2s + 0.5 * a * (2s)^2
Which simplifies to:
d = 4m + 0.5 * a * 4s^2
Now, substitute the value of the acceleration (a) we found earlier and calculate the distance traveled (d). In this case, the distance traveled will be approximately 8.3m.