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What was the initial speed of a car if its speed is $40\frac{m}{s}$ after $5$ seconds of accelerating at $4\frac{m}{s^2}$ ? $\newline$ A. $20\frac{m}{s}$ $\newline$ B. $60\frac{m}{s}$ $\newline$ C. $10\frac{m}{s}$ $\newline$ D. $25\frac{m}{s}$ $\newline$

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Find derivatives using the quotient rule I

Full solution

Q. What was the initial speed of a car if its speed is

40\frac{m}{s}

after

5

seconds of accelerating at

4\frac{m}{s^2}

?

\newline

A.

20\frac{m}{s}

\newline

B.

60\frac{m}{s}

\newline

C.

10\frac{m}{s}

\newline

D.

25\frac{m}{s}

\newline

Use Formula for Final Velocity: Let's use the formula for final velocity, which is $v = u + at$ , where $v$ is the final velocity, $u$ is the initial velocity, $a$ is the acceleration, and $t$ is the time.
Identify Known Values: We know the final velocity $v$ is $40\,\text{m/s}$ , the acceleration $a$ is $4\,\text{m/s}^2$ , and the time $t$ is $5$ seconds. We need to find the initial velocity $u$ .
Plug in Values: Plugging the known values into the formula, we get $40\,\text{m/s} = u + (4\,\text{m/s}^2 \times 5\,\text{s})$ .
Calculate Product: Now, we calculate the product of the acceleration and time: $4 \, \text{m/s}^2 \times 5 \, \text{s} = 20 \, \text{m/s}$ .
Substitute Values: Substitute the product back into the equation: $40\,\text{m/s} = u + 20\,\text{m/s}.$
Solve for Initial Velocity: To find the initial velocity $u$ , we subtract $20\,\text{m/s}$ from both sides of the equation: $u = 40\,\text{m/s} - 20\,\text{m/s}$ .
Final Answer: After the subtraction, we find that the initial velocity $u$ is $20$ m/s.

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