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

Step-by-step 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`