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): $$5(2)^2 + 25(2) = 20 + 50 = 70.$$