A cart rolling down an incline for 5.0 seconds has an acceleration of 4.0 m/s2
. If the cart has a beginning
speed of 2.0 m/s, what is its final speed?
To find the final speed of the cart rolling down an incline, we can use the equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity (unknown)
u = initial velocity (2.0 m/s)
a = acceleration (4.0 m/s^2)
s = displacement (unknown)
Since the cart is rolling down the incline, we can assume that the displacement is caused by gravity and can be calculated using the equation:
s = ut + (1/2)at^2
where:
t = time (5.0 seconds)
Substituting the values into the equation, we have:
s = (2.0 m/s)(5.0 s) + (1/2)(4.0 m/s^2)(5.0 s)^2
= 10.0 m + (1/2)(4.0)(25.0)
= 10.0 m + 50.0 m
= 60.0 m
Now, we can substitute the values of u, a, and s into the first equation to find the final velocity:
v^2 = (2.0 m/s)^2 + 2(4.0 m/s^2)(60.0 m)
= 4.0 m/s + 480.0 m^2/s^2
= 484.0 m^2/s^2
To find v, we take the square root of both sides of the equation:
v = √(484.0 m^2/s^2)
= 22.0 m/s
Therefore, the final speed of the cart rolling down the incline after 5.0 seconds is 22.0 m/s.