# Math Help - Kinematics question.

1. ## Kinematics question.

right can anyone tell me the answer to this question:

A train travels along a track and its speed (in miles per hour) is given as s(t)=40t for the first half hour of travel. Its speed is equal and constant to s(t)=40/2 after the first half hour. Here time t is measured in hours. How far (in miles) does the train travel in the first hour of travel? Just give numerical value

2. ## Re: Kinematics question.

Right you will need to do some very simple integrating to do this, we know the speed of the train so remember how the velocity is related to speed and distance
$s(t) = \frac{dx}{dt}$

we therefore need to integrate this to find:
$x = \int_{t=0}^1 s(t) dt = \int_{0}^{0.5} 40 t dt + \int_{0.5}^1 20 dt$

can you finish from here?