91影视

The rate with which the body changes its velocity in a given amount of time is known as acceleration. The acceleration of a body can mathematically be defined as the double derivative of the velocity with respect to time.

Given data.

The initial velocity of the automobile is $v_1鈥�=鈥�65鈥�\frac{\mathrm{km}}{\mathrm{h}}$.

The final velocity of the automobile is $v_2鈥�=鈥�120鈥�\frac{\mathrm{km}}{\mathrm{h}}$.

The acceleration of the automobile is $a鈥�=鈥�1.8鈥�\frac{\mathrm{m}}{{\mathrm{s}}^2}$.

Assumption.

Assume that it takes t time to accelerate from $65\frac{\mathrm{km}}{\mathrm{h}}$to $120\frac{\mathrm{km}}{\mathrm{h}}$.

You know that the acceleration is

role="math" localid="1642768787969" $a鈥�=鈥�\frac{v_2鈥�-鈥�v_1}{螖t}鈥�\left(i\right)$.

Now,

$\begin{array}{c}{v}_1鈥�=鈥�5鈥�\frac{\mathrm{km}}{\mathrm{h}}\\ =鈥�65鈥�\frac{\mathrm{km}}{\mathrm{h}}鈥�脳鈥�\frac{1000鈥�\mathrm{m}}{1鈥�\mathrm{km}}鈥�脳鈥�\frac{1鈥�\mathrm{h}}{3600鈥�\mathrm{s}}\\ =鈥�18.06鈥�\frac{\mathrm{m}}{\mathrm{s}}\end{array}$,

And,

$\begin{array}{c}{v}_2鈥�=鈥�120鈥�\frac{\mathrm{km}}{\mathrm{h}}\\ =鈥�120\frac{\mathrm{km}}{\mathrm{h}}鈥�脳鈥�\frac{1000鈥�\mathrm{m}}{1鈥�\mathrm{km}}鈥�脳鈥�\frac{1鈥�\mathrm{h}}{3600鈥�\mathrm{s}}\\ =鈥�33.33鈥�\frac{\mathrm{m}}{\mathrm{s}}\end{array}$

Now, substituting all the values of $v_1,v_2$and $a$in equation (i),

$\begin{array}{c}1.8鈥�\frac{\mathrm{m}}{{\mathrm{s}}^2}=\frac{33.33鈥�\frac{\mathrm{m}}{\mathrm{s}}鈥�-鈥�18.06鈥�\frac{\mathrm{m}}{\mathrm{s}}}{螖t}\\ 螖t=鈥�\frac{33.33鈥�\frac{\mathrm{m}}{\mathrm{s}}鈥�-鈥�18.06鈥�\frac{\mathrm{m}}{\mathrm{s}}}{1.8鈥�\frac{\mathrm{m}}{{\mathrm{s}}^2}鈥�}\\ 螖t=鈥�8.48鈥�\mathrm{s}\end{array}$

Therefore, it takes 8.48 s to accelerate from $65\frac{\mathrm{km}}{\mathrm{h}}$to $120\frac{\mathrm{km}}{\mathrm{h}}$.