Question

1. a car increases velocity from 10 m/s to 30 m/s in 5 seconds. what is its acceleration?
2. a 25 kg object accelerates at 3 m/s². what is the net force?
3. a 90 n force moves a cart with an acceleration of 6 m/s². what is the carts mass?

Explanation:

Step1: Recall acceleration formula

The formula for acceleration $a=\frac{v - u}{t}$, where $v$ is final - velocity, $u$ is initial - velocity and $t$ is time. Given $u = 10\ m/s$, $v = 30\ m/s$ and $t = 5\ s$.
$a=\frac{30 - 10}{5}$

Step2: Calculate acceleration

$a=\frac{20}{5}=4\ m/s^{2}$

Step3: Recall force formula for second question

The formula for force $F=ma$, where $m$ is mass and $a$ is acceleration. Given $m = 25\ kg$ and $a = 3\ m/s^{2}$.
$F=25\times3$

Step4: Calculate force

$F = 75\ N$

Step5: Recall mass formula for third question

The formula for mass $m=\frac{F}{a}$, where $F$ is force and $a$ is acceleration. Given $F = 90\ N$ and $a = 6\ m/s^{2}$.
$m=\frac{90}{6}$

Step6: Calculate mass

$m = 15\ kg$

Answer:

1. $4\ m/s^{2}$
2. $75\ N$
3. $15\ kg$