A remote control toy car starts from rest and moves with constant unkown acceleration. After half a second it has travel 0.65m. How far has it traveled after 3 seconds?
Vf^2=2ad
vf=at
so
(at)^2=2ad
a=2d/t^2=2*.65/(.5)^2
Now that you know a,
vf=at when t is three
and the distance it has went is
1/2 vf*time
To solve this problem, we can use the equations of motion for uniformly accelerated motion.
The first equation is:
S = ut + (1/2)at^2
Where:
S = distance travelled
u = initial velocity (which is zero in this case as the toy car starts from rest)
a = acceleration
t = time taken
We are given that the car has traveled a distance of 0.65m in 0.5 seconds. Plugging these values into the equation, we can solve for the acceleration (a):
0.65 = 0 + (1/2)a(0.5)^2
0.65 = (1/8)a
a = 8 * 0.65
a = 5.2 m/s^2
Now, we can use this value of acceleration to find the distance traveled after 3 seconds:
S = ut + (1/2)at^2
S = 0 + (1/2)(5.2)(3)^2
S = 0 + (1/2)(5.2)(9)
S = 0 + 23.4
S = 23.4 m
Therefore, the toy car will have traveled a distance of 23.4 meters after 3 seconds.