A car is accelerating in a straight line so that its velocity in metres per second is equal to the square root of the time elapsed, measured in seconds. How far has the car travelled in the first hour?
A) 144 km
B) 120 km
C) 244 km
D) 344 km
E) 169 km

Question

Quizplus · Accepted Answer

The velocity of the car is given by v(t) = √t. To find the distance travelled, we need to integrate the velocity function with respect to time from 0 to 3600 seconds (since 1 hour = 3600 seconds). The integral of √t is (2/3)t^(3/2). Evaluating this from 0 to 3600 gives (2/3)(3600)^(3/2) = 144000 meters, which is 144 km.

A Car Is Accelerating in a Straight Line So That