A remote-control vehicle moves forward with constant acceleration. During the first two seconds, it
travels 55.0(cm), and during the following two seconds, another 77.0(cm)
(a) Calculate the vehicle’s initial velocity and its acceleration.
(b) What distance will it travel the next 4.0(s)?
.55 = Vi(2) + (1/2) a 2^2
0.55 = 2 Vi + 2 a
total distance after 4 seconds = .55+.77
= 1.32 m
1.32 = 4 Vi + (1/2) a (4^2)
1.32 = 4 Vi + 8 a
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so solve these two equations for Vi and a:
1.32 = 4 Vi + 8 a
0.55 = 2 Vi + 2 a
thank you so much Damon!
To solve this problem, we can use the equations of motion, which relate the initial velocity, final velocity, acceleration, and distance traveled.
(a) To calculate the initial velocity and acceleration, we'll need to use the equations of motion that include the variables we have: distance, time, initial velocity, and acceleration.
The equation we can use is:
2as = vf^2 - vi^2
Where:
a = acceleration,
s = distance traveled,
vf = final velocity,
vi = initial velocity.
In the first two seconds, the distance traveled is 55 cm, and during the next two seconds, it travels another 77 cm.
For the first two seconds (t = 2s), we have:
s = 55 cm
t = 2s
Plugging these values into the equation, we have:
2a * (2 s) = vf^2 - vi^2
Since it is moving with constant acceleration, we can assume vf = vi + at, where t is the time.
So, after solving:
4a = vf^2 - vi^2 --(1)
Using the next two seconds (t = 4s), we have:
s = 77 cm
t = 4s
Plugging these values into the same equation, we get:
8a = vf^2 - vi^2 --(2)
We now have two equations with two unknowns (vi and a). We can solve this system of equations to find the values.
To make the calculations easier, let's subtract equation (1) from equation (2):
8a - 4a = vf^2 - vi^2 - (vf^2 - vi^2)
4a = 0
Therefore, a = 0 cm/s^2
Now, using equation (1) with a = 0:
4(0) = vf^2 - vi^2
0 = vf^2 - vi^2
Since both terms have the same sign, they must both be zero.
So, vi = vf = 0 cm/s
Therefore, the vehicle's initial velocity is 0 cm/s, and its acceleration is 0 cm/s^2.
(b) To find the distance it will travel in the next 4.0 seconds, we can use the equation of motion:
s = vit + 0.5at^2
Given that the initial velocity (vi) and acceleration (a) are both 0, we are left with:
s = 0(4s) + 0.5(0)(4s)^2
s = 0 + 0
s = 0
Therefore, the vehicle will travel a distance of 0 cm in the next 4.0 seconds.