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. 70
• B. 140
• C. 35
• D. 60
• E. 55

Hint:

When calculating distance from velocity, integrate the velocity function over the time interval.

Answer 1

The Correct Option is A

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): \[ 5(2)^2 + 25(2) = 20 + 50 = 70. \]