At time t seconds, the velocity (in m/s) of a bead sliding on a wire is given by the equation: v (t) = 4t³-3t². Please find the distance, in meters, travelled by the bead between the times t=1s and t=3s ?
Answers
Answer:
54
Explanation:
integrate v with t and plug in 3 and 1
Answer: The distance is 54 meters.
Explanation:
To find the distance travelled by the bead between the times t=1s and t=3s, we need to integrate the given velocity function with respect to time over the given interval of time. The integral of the velocity function gives the displacement, which is the total distance travelled by the bead.
The velocity function v(t) is given as v(t) = 4t³-3t².
To find the displacement, we need to integrate v(t) with respect to t from t=1 to t=3:
∫(v(t))dt = ∫(4t³-3t²)dt
= (4/4)t⁴ - (3/3)t³ + C
= t⁴ - t³ + C
Evaluating this integral from t=1 to t=3 gives us the displacement, or the distance travelled by the bead between those times:
= [(3)⁴ - (3)³] - [(1)⁴ - (1)³]
= (81-27) - (1-1)
= 54 meters