Question

A cart is given an initial velocity of 2 m/s and experiences a constant acceleration of 2 m/s2. What is the magnitude of the cart's displacement during the first 6 s of its motion?

Answer 1

Answer: 48 m

Explanation:

Since we are dealing with constant acceleration, we can use the following equations:

$V=V_{o}+a.t$ (1)

$V^{2}={V_{o}}^{2}+2ad$ (2)

Where:

$V$ is the cart’s final velocity

$V_{o}=2 m/s$ is the cart’s initial velocity

$a=2 m/s^{2}$ is the cart's acceleration

$t=6 s$ is the time

$d$ is the cart's displacement

So, firstly we have to find $V$ from (1):

$V=2 m/s+(2 m/s^{2})(6 s)$ (3)

$V=14 m/s$ (4)

Isolating $d$ from (2) and substituting (4):

$d=\frac{V^{2}-V_{o}}^{2}}{2a}$ (5)

$d=\frac{(14 m/s)^{2}-(2 m/s)}^{2}}{2(2 m/s^{2})}$ (6)

Finally:

$d=48 m$