Answer:
a)8.59 m/s
b)-0.8818 m/s²
Explanation:
a) Given the van moved 40 m in 7.70 seconds to a final velocity of 1.80 m/s
Apply the equation for motion;
[tex]d=(\frac{V_i+V_f}{2} )*t[/tex]
where
t=time the object moved
d=displacement of the object
Vi=initial velocity
Vf=final velocity
Given
t=7.70s
Vf=1.80 m/s
d=40m
Vi=?
Substitute values in equation
[tex]40=(\frac{V_i+1.80}{2} )7.70\\\\\\40=\frac{7.70V_i+13.86}{2} \\\\80=7.70V_i+13.86\\\\80-13.86=7.70V_i\\\\66.14=7.70V_i\\\\\frac{66.14}{7.70} =\frac{7.70V_i}{7.70} \\8.59=V_i[/tex]
b)Acceleration is the rate of change in velocity
Apply the formula
Vf=Vi+at
where;
Vf=final velocity of object
Vi=Initial velocity of the object
a=acceleration
t=time the object moved
Substitute values in equation
Given;
Vf=1.80 m/s
Vi=8.59 m/s
t=7.70 s
a=?
Vf=Vi+at
1.80=8.59+7.70a
1.80-8.59=7.70a
-6.79=7.70a
-6.79/7.70=7.70a/7.70
-0.8818=a
The van was slowing down.
When the brakes are applied to a moving van, it travels a distance of 40.0 m in 7.70 s with a final velocity of 1.80 m/s.
a) The initial speed of the van just before the brakes were applied was 8.59 m/s.
b) The acceleration of the van while the brakes were applied was -0.88 m/s².
a) The initial speed of the van can be calculated as follows:
[tex] v_{f} = v_{i} + at [/tex]
Where:
[tex] v_{f}[/tex]: is the final velocity = 1.80 m/s
[tex] v_{i}[/tex]: is the initial velocity =?
a: is the acceleration
t: is the time = 7.70 s
By solving the above equation for a we have:
[tex] a = \frac{v_{f} - v_{i}}{t} [/tex] (1)
Now, we need to use other kinematic equation to find the initial velocity.
[tex] v_{i}^{2} = v_{f}^{2} - 2ad [/tex] (2)
By entering equation (1) into (2) we have:
[tex] v_{i}^{2} = v_{f}^{2} - 2d(\frac{v_{f} - v_{i}}{t}) = (1.80 m/s)^{2} - 2*40.0 m(\frac{1.80 m/s - v_{i}}{7.70 s}) [/tex]
After solving the above equation for [tex]v_{i}[/tex] we get:
[tex] v_{i} = 8.59 m/s [/tex]
Hence, the initial velocity is 8.59 m/s.
b) The acceleration can be calculated with equation (1):
[tex] a = \frac{v_{f} - v_{i}}{t} = \frac{1.80 m/s - 8.59 m/s}{7.70 s} = -0.88 m/s^{2} [/tex]
Then, the acceleration is -0.88 m/s². The minus sign is because the van is decelerating.
You can find more about acceleration here: https://brainly.com/question/2239252?referrer=searchResults
I hope it helps you!
