To solve this problem, we can use the equations of motion for uniformly accelerated motion. We'll use the equation that relates displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t):
s = ut + (1/2)at^2
In this case, the car starts from rest, so the initial velocity (u) is 0 m/s. The final velocity (v) is 4 m/s, the displacement (s) is 10 m, and we need to find the time (t).
Using the equation of motion, we can rearrange it to solve for time:
s = (1/2)at^2
10 = (1/2)at^2
Multiplying both sides by 2:
20 = at^2
Dividing both sides by a:
t^2 = 20/a
Taking the square root of both sides:
t = sqrt(20/a)
We need to find the value of acceleration (a). Since the car rolls down the ramp without slipping, the acceleration can be calculated using the following equation:
v^2 = u^2 + 2as
Substituting the given values:
(4 m/s)^2 = (0 m/s)^2 + 2a(10 m)
16 = 20a
Dividing both sides by 20:
a = 16/20 = 0.8 m/s^2
Now, we can substitute the value of acceleration into the equation for time:
t = sqrt(20/0.8) = sqrt(25) = 5 seconds
Therefore, it took the toy car 5 seconds to roll down the 10 m long ramp.