Question

.An automobile accelerates uniformly from 0 to 24 m/s in 6.0 s. If the car has a massof 2.0x10^3kg, what is the force accelerating it?

Answer 1

8000 Newtons

Step 1

find the acceleration

the acceleration can be calculated by using the formula:

$a=\frac{\Delta velocity}{\Delta time}=\frac{v_f-v_1}{\text{time taken}}$

then,let

$\begin{gathered} v_i=0 \\ v_f=\text{ 24}\frac{m}{s} \\ \text{time}=\text{ 6 sec} \end{gathered}$

now, replace in the formula

$\begin{gathered} a=\frac{\Delta velocity}{\Delta time}=\frac{v_f-v_1}{\text{time taken}} \\ a=\frac{24\frac{m}{s}-0\frac{m}{s}}{6\text{ s}} \\ a=4\frac{m}{s^2} \end{gathered}$

Step 2

find the force.

Newton's Second Law of Motion says that acceleration happens when a force acts on a mass (object), it is given by:

$\begin{gathered} F=\text{ ma} \\ \text{where m is the mass} \\ \text{and a is the acceleration} \end{gathered}$

then, let

$\begin{gathered} m=2.0\cdot10^3\operatorname{kg} \\ a=4\text{ }\frac{m}{s^2} \end{gathered}$

now, replace

$\begin{gathered} F=ma \\ F=2.0\cdot10^3\operatorname{kg}\cdot4\frac{m}{s^2} \\ F=8000\text{ Newtons} \end{gathered}$

therefore , the answer is

8000 Newtons

I hope this helps you