A Porsche challenges a Honda to a 400 m race. Because the Porsche’s acceleration of 3.5 m/s² is larger than the Honda’s 3.0 m/s² , the Honda gets a 1.0 s head start. Who wins? By how many seconds?

The acceleration of Porsche is 3.5m/s²
Similarly, the acceleration of Honda is 3.0 m/s²

Honda gets the head start of 1 sec

Write the equation of motion,

$S=v_{i}t+\frac{1}{2}a{t}^2$

Substitute values of all variable in the above expression to obtain the value of time $t$
$$\begin{gathered} 400=\left(0\right)t+\frac{1}{2}(3.5)t^2 \\ 400=1.75t^2 \\ {t}^2=228.5 \\ \Rightarrow t=15.12sec \end{gathered}$$
Thus, the time taken by Porsche to finish the race is 15.12 sec.

Honda is given head start of 1 sec.

Let the distance travelled by Honda in 1 sec is $d$

Write the equation of motion
$d=v_{i}t+\frac{1}{2}a{t}^2$

Substitute the values of variable sin the above equation to obtain the value of $d$
localid="1648463980695" $d=0\left(1\right)+\frac{1}{2}(3.0){\left(1\right)}^2=\frac{3}{2}=1.5m$
This is the distance travelled by Honda in 1 sec head start.
Now, to find velocity of the car in head start time 1sec, write the equation of motion
$v_f=v_i+at$

Substitute the values of variables in the above equation

$$\begin{gathered} v_f=0+\left(3\right)\left(1\right) \\ {v}_f=3m/s \end{gathered}$$

The distance remained to cover after head start is $(400-d)m$as shown in the figure. Hence, plug the value $d$, to find the distance remained (S')

$$\begin{gathered} S\text{'}=400-1.5 \\ =398.5m \end{gathered}$$

Now, to find the time taken by Honda to finish the race, write the equation of motion

$S\text{'}=v_{i}t+\frac{1}{2}a{t}^2$

It should be observed that the initial velocity of car would be equal to the final velocity attained by car after a head start. Therefore, $v_i=v_f=3m/s$. Now, plug the values of all the variables in the above equation of motion

localid="1648020104703" $$\begin{gathered} 398.5=3\left(t\right)+\frac{1}{2}\left(3\right)t^2 \\ 398.5=3t+1.5t^2 \end{gathered}$$

Using quadratic equation formula, solve for t to get

$t=15.32s$

Therefore, the time taken by Honda to finish the race is 15.32 sec

Time taken by Porsche is 15.12 sec
The time taken by Honda is more than Porsche , hence Porsche wins the race by 0.2 sec.