# 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.