Question

A box cart is pushed and given an initial velocity of 2.0 m/s and undergoes a constant acceleration of 2.0 m/s2 . What is the magnitude of the box cart's displacement after the first 6.0 s of its motion?

Answer 1

The magnitude of the displacement of a box cart that is pushed and given an initial velocity of 2.0 m/s with a constant acceleration of 2.0 m/s2 after the first 6.0 s can be calculated using the kinematic equation for displacement, the box cart's displacement after 6.0 s is found to be 84.0 meters.

Step-by-step explanation:

Using the kinematic equation for displacement, s = ut + (1/2)at^2,:

s = ut + \(\frac{1}{2}\)at2

Where:
s is the displacement,
u is the initial velocity (2.0 m/s),
a is the acceleration (2.0 m/s2),
t is the time (6.0 s).

Substituting the given values:

s = (2.0 m/s)(6.0 s) + \(\frac{1}{2}\)(2.0 m/s2)(6.0 s)2

s = 12.0 m + (1)(2.0 m/s2)(36.0 s2)

s = 12.0 m + (1)(72.0 m)

s = 12.0 m + 72.0 m

s = 84.0 m

The box cart's displacement after 6.0 s is 84.0 meters.