Question:
A train starts from X towards Y at 3 pm (time \( t = 0 \)) with velocity \( v(t) = 10t + 25 \) km per hour, where \( t \) is measured in hours.
Then the distance covered by the train at 5 pm (in km) is:
A train starts from X towards Y at 3 pm (time \( t = 0 \)) with velocity \( v(t) = 10t + 25 \) km per hour, where \( t \) is measured in hours.
Then the distance covered by the train at 5 pm (in km) is:
Show Hint
When calculating distance from velocity, integrate the velocity function over the time interval.
Updated On: Apr 7, 2026
- 70
- 140
- 35
- 60
- 55
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1:
The distance covered by the train is the integral of the velocity function:
\[
{Distance} = \int_0^2 (10t + 25) \, dt.
\]
Step 2:
Integrating \( 10t + 25 \):
\[
\int (10t + 25) \, dt = 5t^2 + 25t.
\]
Step 3:
Evaluating the integral at \( t = 2 \) (since 5 pm corresponds to 2 hours after 3 pm):
\[
5(2)^2 + 25(2) = 20 + 50 = 70.
\]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Integration Questions
- \(\int\frac{e^{\frac{1}{\sqrt t}}}{t\sqrt t}dt=\)
- \(\int\frac{1}{x^3}\sqrt{1-\frac{1}{x^2}}dx=\)
- \(\int(\tan^2(2x)-\cot^2(2x))dx=\)
- \(\int\sin^3xdx+\int\cos^2x\sin xdx=\)
- \(\int\frac{dx}{x^2-x}=\)
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions