A net force of 15 N is applied to a cart with a mass of 2.1 kg. a. What is the acceleration of the cart? b. How long will it take the cart to travel 2.8 m, starting from rest?
a. To find the acceleration of the cart, we can use Newton's second law of motion:
F = ma
Where:
F = net force applied (15 N)
m = mass of the cart (2.1 kg)
a = acceleration
Rearranging the formula to solve for acceleration:
a = F/m
a = 15 N / 2.1 kg
a ≈ 7.14 m/s^2
Therefore, the acceleration of the cart is approximately 7.14 m/s^2.
b. To find how long it will take for the cart to travel 2.8 m, starting from rest, we can use the kinematic equation:
d = (1/2)at^2
Where:
d = distance traveled (2.8 m)
a = acceleration (7.14 m/s^2, calculated in part a)
t = time
Rearranging the equation to solve for time:
t = sqrt(2d/a)
t = sqrt( (2 * 2.8 m) / 7.14 m/s^2 )
t = sqrt( 5.6 / 7.14 )
t ≈ sqrt(0.784)
t ≈ 0.886 s
Therefore, it will take approximately 0.886 seconds for the cart to travel 2.8 m starting from rest.