A space vehicle accelerates uniformly from 70 at t = 0 to 172 at t = 10.0. How far did it move between = 2.0 and = 6.0 ?
So I used the forumla d=vt+.5a(t)^2
but for a i got 10.2 since a=(172-70)/10
Now im stuck for v, what do i put for v?
no units, no sense.
To find the distance the space vehicle moved between t=2.0 and t=6.0, you can use the formula d = vt + 0.5at^2.
In this formula, v represents the initial velocity of the vehicle at t=2.0. Since the problem states that the vehicle accelerated uniformly from 70 m/s at t=0 to 172 m/s at t=10.0, we can assume that the initial velocity at t=2.0 is the same as the average velocity between t=0 and t=10.0.
To find the average velocity, you can use the formula:
average velocity = (final velocity - initial velocity) / (final time - initial time)
Plugging in the given values:
average velocity = (172 m/s - 70 m/s) / (10.0 s - 0 s)
= 102 m/s / 10.0 s
= 10.2 m/s
So, you can use v = 10.2 m/s in the formula d = vt + 0.5at^2 to find the distance the vehicle moved between t=2.0 and t=6.0.
To find the displacement between t = 2.0 s and t = 6.0 s, you are correct in using the formula d = vt + 0.5at². However, to determine the displacement during this time interval, you need to find the values of v and a at t = 2.0 s.
Since the space vehicle is accelerating uniformly, you can use the formula for uniformly accelerated motion: v = u + at, where u is the initial velocity.
To find the value of u, you can use the given information that the space vehicle accelerates from 70 m/s at t = 0 s. Therefore, at t = 2.0 s, the speed (v) of the vehicle would have increased from u to u + 2a.
Now, using the equation v = u + at, the velocity at t = 2.0 s is:
v = u + at
v = (u + 2a)
Substituting the given values:
70 m/s = u + (10.2 m/s²)(2.0 s)
Now you can solve for u:
70 m/s - (20.4 m/s²) = u
u = 70 m/s - 20.4 m/s²
u = 49.6 m/s
So, the initial velocity of the vehicle at t = 2.0 s is 49.6 m/s.
Now that you have the initial velocity (u) and acceleration (a), you can calculate the displacement by using the formula:
d = vt + 0.5at²
Substituting the values, the displacement between t = 2.0 s and t = 6.0 s is:
d = (49.6 m/s)(4.0 s) + 0.5(10.2 m/s²)(4.0 s)²
Now you can solve this equation to find the displacement.