Question

Allison exerts a steady net force of 54 N on a 24-kg

shopping cart initially at rest for 2.6 s. find the distance.

Answer 1

Approximately
`7.6\; {\rm m}` while the force was applied.

Step-by-step explanation:

Divide net force by mass to find acceleration:

`\begin{aligned}(\text{acceleration}) &= \frac{(\text{net force})}{(\text{mass})} = 2.25\; {\rm m\cdot s^(-2)}\end{aligned}`.

(Note that
`1\; {\rm N} = 1\; {\rm kg\cdot m\cdot s^(-2)}`.)

The question states that this acceleration of
`a = 2.25\; {\rm m\cdot s^(-2)}` continued for
`t = 2.6\; {\rm s}`. Additionally, it is given that initial velocity was
`u = 0\; {\rm m\cdot s^(-1)}` (initially at rest.)

Let
`x` denote the distance travelled. Apply the SUVAT equation
`x = (1/2)\, a\, t^(2) + u\, t` to find this distance:

`\begin{aligned}x &= (1)/(2)\, a\, t^(2) + u\, t \\ &= (1)/(2)\, (2.25)\, (2.6)^(2)\; {\rm m} + (0)\, (2.6)\; {\rm m} \\ &= (1)/(2)\, (2.25)\, (2.6)^(2)\; {\rm m} \\ &\approx 7.6\; {\rm m}\end{aligned}`.