The acceleration of a particle is defined by equation, a = - 8m/s2 .
Knowing that x = 20m where t = 4s and that x = 4m where v = 16m/s,
Determine,
The time when the velocity is zero, [6]
The velocity and the total distance travelled when t = 11s [4]
a = -8
v = -8t+c1
x = -4t^2 + c1*t + c2
using the two data points,
when t = (c1-16)/8, v = 16
-4*16 + 4*c1 + c2 = 20
-4*((c1-16)/8)^2 + (c1-16)/8 * c1 + c2 = 4
solving those two equations, we get
c1 = 32, c2 = -44
so we have
v(t) = -8t+32
x(t) = -4t^2 + 32t - 44
Now you can answer the questions.
Well, if the acceleration of a particle is defined by the equation a = -8 m/s^2, then we can start by finding the time when the velocity is zero.
To find the time when the velocity is zero, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Since we're looking for when the velocity is zero, we can set v = 0:
0 = u + (-8) * t
We know that at t = 4s, x = 20m, and at t = 4s, v = 16m/s. So, we can substitute those values into the equation:
16 = u + (-8) * 4
Simplifying, we get:
16 = u - 32
Now we can solve for u:
u = 16 + 32
u = 48 m/s
Now we can substitute the values of u and a into the equation v = u + at to find the time when the velocity is zero:
0 = 48 + (-8) * t
Simplifying, we get:
-48 = -8t
Now we can solve for t:
t = -48 / -8
t = 6s
So, the time when the velocity is zero is 6 seconds.
Now let's move on to finding the velocity and total distance traveled when t = 11s.
To find the velocity, we can use the equation v = u + at. We already know the values of u, a, and t, so we can substitute them into the equation:
v = 48 + (-8) * 11
Simplifying, we get:
v = 48 - 88
v = -40 m/s
So, when t = 11s, the velocity is -40 m/s.
To find the total distance traveled, we can use the equation x = ut + (1/2)at^2. Again, we already know the values of u, a, and t, so we can substitute them into the equation:
x = 48 * 11 + (1/2) * (-8) * (11)^2
Simplifying, we get:
x = 528 + (-44) * 11
x = 528 - 484
x = 44m
So, when t = 11s, the velocity is -40 m/s and the total distance traveled is 44m.
I hope this answer doesn't leave you feeling "negative"!
To solve these problems using the given information, we can use the equations of motion relating acceleration, velocity, and displacement.
1. The time when the velocity is zero (t = ?):
We are given that the acceleration (a) is -8 m/s^2 and the displacement (x) is 4 m when the velocity (v) is 16 m/s.
We can use the equation relating velocity, acceleration, and time:
v = u + at
where u is the initial velocity (which is not given).
Since we know that v = 16 m/s, a = -8 m/s^2, and x = 4 m, we can substitute these values into the equation and solve for u:
16 = u + (-8)(4)
16 = u - 32
u = 16 + 32
u = 48 m/s
Now we can find the time (t) when the velocity is zero using the equation:
v = u + at
0 = 48 + (-8)t
-48 = -8t
t = 6 seconds
Therefore, the time when the velocity is zero is 6 seconds.
2. The velocity and the total distance traveled when t = 11s:
To find the velocity (v) when t = 11s, we can use the equation:
v = u + at
where u is the initial velocity (which is still 48 m/s) and a is the acceleration (-8 m/s^2).
v = 48 + (-8)(11)
v = 48 - 88
v = -40 m/s
Therefore, when t = 11s, the velocity is -40 m/s.
To find the total distance traveled when t = 11s, we can use the equation:
x = ut + (1/2)at^2
x = 48(11) + (1/2)(-8)(11)^2
x = 528 - 48(121)
x = 528 - 5808
x = -5280 m
Therefore, when t = 11s, the total distance traveled is -5280 m.
To solve this problem, we need to use the equations of motion. Let's start by finding the time when the velocity is zero.
1. Time when velocity is zero (t = ?):
We can use the equation of motion relating velocity, acceleration, and time:
v = u + at
Given:
Initial velocity (u) = 16 m/s
Acceleration (a) = -8 m/s^2
Velocity (v) = 0 m/s
0 = 16 + (-8)t
-16 = -8t
t = 2 seconds
Therefore, the time when the velocity is zero is 2 seconds.
2. Velocity and total distance when t = 11 seconds:
To find the velocity when t = 11 seconds, we can use the equation of motion:
v = u + at
Given:
Initial velocity (u) = 16 m/s
Acceleration (a) = -8 m/s^2
Time (t) = 11 seconds
v = 16 + (-8) * 11
v = 16 - 88
v = -72 m/s
Therefore, when t = 11 seconds, the velocity is -72 m/s.
To find the total distance traveled, we can use the equation of motion relating displacement, initial velocity, acceleration, and time:
x = ut + (1/2)at^2
Given:
Initial velocity (u) = 16 m/s
Acceleration (a) = -8 m/s^2
Time (t) = 11 seconds
x = (16 * 11) + (1/2) * (-8) * (11)^2
x = 176 - 44 * 121
x = 176 - 5324
x = -5148 m
Therefore, when t = 11 seconds, the total distance traveled is -5148 m.