A 50 kg cart rests on frictionless surface. A net force of 75 N acts on the carts over a distance of 2m. What maximum speed does the cart reach?
Work: I can figure that the acceleration is 1.5m/s/s, Vi= 0. I was thinking maybe if I found time through the kinematic equation d=Vixt + a/2 X T^2. Then divide the time by distance to get speed. I don't really know. Please Help, Thank you.
why don't you use energy
workin=final KE
75*2=1/2 m v^2
solve for v
To find the maximum speed reached by the cart, you can use the equations of motion.
Given:
Mass of the cart (m) = 50 kg
Net force acting on the cart (F) = 75 N
Distance traveled (d) = 2 m
Initial velocity (Vi) = 0 m/s
Acceleration (a) = F/m = 75 N / 50 kg = 1.5 m/s²
To find the time (t) it takes for the cart to travel the given distance, you can use the kinematic equation:
d = Vi*t + (1/2)*a*t²
Substituting the given values:
2 = 0*t + (1/2)*1.5*t²
2 = (1.5/2)*t²
4/1.5 = t²
t² = 2.6667
t ≈ √(2.6667) ≈ 1.6329 s
Now, to find the maximum speed (Vf) reached by the cart, you can use another kinematic equation:
Vf = Vi + a*t
Substituting the given values:
Vf = 0 + (1.5)*(1.6329)
Vf ≈ 2.4494 m/s
Therefore, the maximum speed reached by the cart is approximately 2.4494 m/s.
To find the maximum speed reached by the cart, you can use the kinematic equation that relates distance, initial velocity, acceleration, and time:
d = vit + (1/2)at^2
In this case, we know the initial velocity (Vi) is 0, and the acceleration (a) is given as 1.5 m/s^2 (the net force acting on the cart divided by its mass). The distance (d) is given as 2 meters. We need to solve for time (t) first and then use it to find the final velocity (Vf).
Rearrange the equation to solve for time:
2 = (1/2)(1.5)t^2
Multiply both sides by 2:
4 = 1.5t^2
Divide both sides by 1.5:
(4/1.5) = t^2
Calculate the value of t^2:
(4/1.5) ≈ 2.67
Now, take the square root of both sides to solve for time (t):
√(4/1.5) ≈ 1.63
So the time taken for the cart to cover a distance of 2 meters is approximately 1.63 seconds.
Next, to find the maximum speed, divide the distance by the time:
maximum speed = distance/time = 2 meters / 1.63 seconds ≈ 1.23 m/s
Therefore, the maximum speed reached by the cart is approximately 1.23 m/s.