If the distance covered by an object in time t is given by s(t) = t^2 + 5t , where s(t) is in meters and t is in seconds, what is the distance covered in the interval between 1 second and 5 seconds?
just figure s(5)-s(1)
To find the distance covered in a given interval, we need to calculate the difference in distance between the ending point and the starting point of the interval.
First, let's find the distance covered at 1 second. Substitute t = 1 into the equation s(t) = t^2 + 5t:
s(1) = 1^2 + 5(1)
s(1) = 1 + 5
s(1) = 6 meters
Next, let's find the distance covered at 5 seconds. Substitute t = 5 into the equation s(t) = t^2 + 5t:
s(5) = 5^2 + 5(5)
s(5) = 25 + 25
s(5) = 50 meters
To find the distance covered in the interval between 1 second and 5 seconds, we subtract the starting distance from the ending distance:
Distance covered = s(5) - s(1)
Distance covered = 50 - 6
Distance covered = 44 meters
Therefore, the distance covered in the interval between 1 second and 5 seconds is 44 meters.